# 11X1 T15 02 finance formulas V2

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Finance FormulaeFinance FormulaeSimple InterestI PRT simple interestI principalP interest rate as a decimal (or fraction)R time periodsT Finance FormulaeSimple InterestI PRT simple interestI principalP interest rate as a decimal (or fraction)R time periodsT e.g. If $3000 is invested for seven years at 6% p.a. simple interest, how much will it be worth after seven years?Finance FormulaeSimple InterestI PRT simple interestI principalP interest rate as a decimal (or fraction)R time periodsT I PRTe.g. If $3000 is invested for seven years at 6% p.a. simple interest, how much will it be worth after seven years?Finance FormulaeSimple InterestI PRT simple interestI principalP interest rate as a decimal (or fraction)R time periodsT I PRT 3000 0.06 7I 1260e.g. If $3000 is invested for seven years at 6% p.a. simple interest, how much will it be worth after seven years?Finance FormulaeSimple InterestI PRT simple interestI principalP interest rate as a decimal (or fraction)R time periodsT I PRT 3000 0.06 7I 1260 Investment is worth $4260 after 7 yearse.g. If $3000 is invested for seven years at 6% p.a. simple interest, how much will it be worth after seven years?Compound Interestnn PRA periodstimeafter amount nAn principalP1 interest rate as a decimal(or fraction)R time periodsn Compound Interestnn PRA periodstimeafter amount nAn principalP1 interest rate as a decimal(or fraction)R time periodsn Note: interest rate and time periods must match the compounding timeCompound Interestnn PRA periodstimeafter amount nAn principalP1 interest rate as a decimal(or fraction)R time periodsn Note: interest rate and time periods must match the compounding timeNote: general term of a geometric seriesCompound Interestnn PRA periodstimeafter amount nAn principalP1 interest rate as a decimal(or fraction)R time periodsn Note: interest rate and time periods must match the compounding timee.g. If $3000 is invested for seven years at 6% p.a, how much will it be worth after seven years if;a) compounded annually?Note: general term of a geometric seriesCompound Interestnn PRA periodstimeafter amount nAn principalP1 interest rate as a decimal(or fraction)R time periodsn Note: interest rate and time periods must match the compounding timee.g. If $3000 is invested for seven years at 6% p.a, how much will it be worth after seven years if;a) compounded annually?nnA PRNote: general term of a geometric seriesCompound Interestnn PRA periodstimeafter amount nAn principalP1 interest rate as a decimal(or fraction)R time periodsn Note: interest rate and time periods must match the compounding timee.g. If $3000 is invested for seven years at 6% p.a, how much will it be worth after seven years if;a) compounded annually?nnA PR 77 3000 1.06A 7 4510.89A Note: general term of a geometric seriesCompound Interestnn PRA periodstimeafter amount nAn principalP1 interest rate as a decimal(or fraction)R time periodsn Note: interest rate and time periods must match the compounding timee.g. If $3000 is invested for seven years at 6% p.a, how much will it be worth after seven years if;a) compounded annually?nnA PR 77 3000 1.06A 7 4510.89A Investment is worth $4510.89 after 7 yearsNote: general term of a geometric seriesCompound Interestnn PRA periodstimeafter amount nAn principalP1 interest rate as a decimal(or fraction)R time periodsn Note: interest rate and time periods must match the compounding timee.g. If $3000 is invested for seven years at 6% p.a, how much will it be worth after seven years if;a) compounded annually?nnA PR 77 3000 1.06A 7 4510.89A Investment is worth $4510.89 after 7 yearsb) compounded monthly?Note: general term of a geometric seriesCompound Interestnn PRA periodstimeafter amount nAn principalP1 interest rate as a decimal(or fraction)R time periodsn Note: interest rate and time periods must match the compounding timee.g. If $3000 is invested for seven years at 6% p.a, how much will it be worth after seven years if;a) compounded annually?nnA PR 77 3000 1.06A 7 4510.89A Investment is worth $4510.89 after 7 yearsb) compounded monthly?nnA PRNote: general term of a geometric seriesCompound Interestnn PRA periodstimeafter amount nAn principalP1 interest rate as a decimal(or fraction)R time periodsn Note: interest rate and time periods must match the compounding timee.g. If $3000 is invested for seven years at 6% p.a, how much will it be worth after seven years if;a) compounded annually?nnA PR 77 3000 1.06A 7 4510.89A Investment is worth $4510.89 after 7 yearsb) compounded monthly?nnA PR 8484 3000 1.005A 84 4561.11A Note: general term of a geometric seriesCompound Interestnn PRA periodstimeafter amount nAn principalP1 interest rate as a decimal(or fraction)R time periodsn Note: interest rate and time periods must match the compounding timee.g. If $3000 is invested for seven years at 6% p.a, how much will it be worth after seven years if;a) compounded annually?nnA PR 77 3000 1.06A 7 4510.89A Investment is worth $4510.89 after 7 yearsb) compounded monthly?nnA PR 8484 3000 1.005A 84 4561.11A Investment is worth $4561.11 after 7 yearsNote: general term of a geometric seriesDepreciationnn PRA periodstimeafter amount nAn principalP1 depreciation rate as a decimal(or fraction)R time periodsn Depreciationnn PRA periodstimeafter amount nAn principalP1 depreciation rate as a decimal(or fraction)R time periodsn Note: depreciation rate and time periods must match the depreciation timeDepreciationnn PRA periodstimeafter amount nAn principalP1 depreciation rate as a decimal(or fraction)R time periodsn Note: depreciation rate and time periods must match the depreciation timee.g. An espresso machine bought for $15000 on 1st January 2001 depreciates at a rate of 12.5%p.a.a) What will its value be on 1st January 2010?Depreciationnn PRA periodstimeafter amount nAn principalP1 depreciation rate as a decimal(or fraction)R time periodsn Note: depreciation rate and time periods must match the depreciation timee.g. An espresso machine bought for $15000 on 1st January 2001 depreciates at a rate of 12.5%p.a.a) What will its value be on 1st January 2010?nnA PRDepreciationnn PRA periodstimeafter amount nAn principalP1 depreciation rate as a decimal(or fraction)R time periodsn Note: depreciation rate and time periods must match the depreciation timee.g. An espresso machine bought for $15000 on 1st January 2001 depreciates at a rate of 12.5%p.a.a) What will its value be on 1st January 2010?nnA PR 99 15000 0.875A 9 4509.87A Depreciationnn PRA periodstimeafter amount nAn principalP1 depreciation rate as a decimal(or fraction)R time periodsn Note: depreciation rate and time periods must match the depreciation timee.g. An espresso machine bought for $15000 on 1st January 2001 depreciates at a rate of 12.5%p.a.a) What will its value be on 1st January 2010?nnA PR 99 15000 0.875A 9 4509.87A Machine is worth $4509.87 after 9 yearsb) During which year will the value drop below 10% of the original cost?b) During which year will the value drop below 10% of the original cost?nn PRA b) During which year will the value drop below 10% of the original cost? 15000 0.875 1500n nn PRA b) During which year will the value drop below 10% of the original cost? 15000 0.875 1500n 0.875 0.1n log 0.875 log0.1n log0.875 log0.1n log 0.1log 0.875n 17.24377353n nn PRA b) During which year will the value drop below 10% of the original cost? 15000 0.875 1500n 0.875 0.1n log 0.875 log0.1n log0.875 log0.1n log 0.1log 0.875n 17.24377353n during the 18th year (i.e. 2018) its value will drop to 10% the original costnn PRA Investing Money by Regular Instalments2002 HSC Question 9b)A superannuation fund pays an interest rate of 8.75% p.a. which compounds annually. Stephanie decides to invest $5000 in the fund at the beginning of each year, commencing on 1 January 2003.What will be the value of Stephanies superannuation when she retires on 31 December 2023?(4)Investing Money by Regular Instalments2002 HSC Question 9b)A superannuation fund pays an interest rate of 8.75% p.a. which compounds annually. Stephanie decides to invest $5000 in the fund at the beginning of each year, commencing on 1 January 2003.What will be the value of Stephanies superannuation when she retires on 31 December 2023?(4) 2121 5000 1.0875A amount invested for 21 yearsInvesting Money by Regular Instalments2002 HSC Question 9b)A superannuation fund pays an interest rate of 8.75% p.a. which compounds annually. Stephanie decides to invest $5000 in the fund at the beginning of each year, commencing on 1 January 2003.What will be the value of Stephanies superannuation when she retires on 31 December 2023?(4) 2121 5000 1.0875A amount invested for 21 years 2020 5000 1.0875A amount invested for 20 yearsInvesting Money by Regular Instalments2002 HSC Question 9b)A superannuation fund pays an interest rate of 8.75% p.a. which compounds annually. Stephanie decides to invest $5000 in the fund at the beginning of each year, commencing on 1 January 2003.What will be the value of Stephanies superannuation when she retires on 31 December 2023?(4) 2121 5000 1.0875A amount invested for 21 years 2020 5000 1.0875A amount invested for 20 years 1919 5000 1.0875A amount invested for 19 yearsInvesting Money by Regular Instalments2002 HSC Question 9b)A superannuation fund pays an interest rate of 8.75% p.a. which compounds annually. Stephanie decides to invest $5000 in the fund at the beginning of each year, commencing on 1 January 2003.What will be the value of Stephanies superannuation when she retires on 31 December 2023?(4) 2121 5000 1.0875A amount invested for 21 years 2020 5000 1.0875A amount invested for 20 years 1919 5000 1.0875A amount invested for 19 years 11 5000 1.0875A amount invested for 1 yearInvesting Money by Regular Instalments 21 20Amount 5000 1.0875 5000 1.0875 5000 1.0875 21 20Amount 5000 1.0875 5000 1.0875 5000 1.0875 5000 1.0875 , 1.0875, 21a r n 21 20Amount 5000 1.0875 5000 1.0875 5000 1.0875 21S 5000 1.0875 , 1.0875, 21a r n 21 20Amount 5000 1.0875 5000 1.0875 5000 1.0875 21S 5000 1.0875 , 1.0875, 21a r n 215000 1.0875 1.0875 10.0875$299604.86 21 20Amount 5000 1.0875 5000 1.0875 5000 1.0875 21S 5000 1.0875 , 1.0875, 21a r n 215000 1.0875 1.0875 10.0875$299604.86c*) Find the year when the fund first exceeds $200000. 21 20Amount 5000 1.0875 5000 1.0875 5000 1.0875 21S 5000 1.0875 , 1.0875, 21a r n 215000 1.0875 1.0875 10.0875$299604.86c*) Find the year when the fund first exceeds $200000. 2Amount 5000 1.0875 5000 1.0875 5000 1.0875 n 21 20Amount 5000 1.0875 5000 1.0875 5000 1.0875 21S 5000 1.0875 , 1.0875, 21a r n 215000 1.0875 1.0875 10.0875$299604.86c*) Find the year when the fund first exceeds $200000. 2Amount 5000 1.0875 5000 1.0875 5000 1.0875 n nS 21 20Amount 5000 1.0875 5000 1.0875 5000 1.0875 21S 5000 1.0875 , 1.0875, 21a r n 215000 1.0875 1.0875 10.0875$299604.86c*) Find the year when the fund first exceeds $200000. 2Amount 5000 1.0875 5000 1.0875 5000 1.0875 n nSi.e 200000nS 5000 1.0875 1.0875 12000000.0875n 5000 1.0875 1.0875 12000000.0875n 2801.0875 1 87n 5000 1.0875 1.0875 12000000.0875n 2801.0875 1 87n 3671.087587n 5000 1.0875 1.0875 12000000.0875n 2801.0875 1 87n 3671.087587n 367log 1.0875 log 87n 5000 1.0875 1.0875 12000000.0875n 2801.0875 1 87n 3671.087587n 367log 1.0875 log 87n 367log 1.0875 log87n 5000 1.0875 1.0875 12000000.0875n 2801.0875 1 87n 3671.087587n 367log 1.0875 log 87n 367log 1.0875 log87n 367log87log 1.0875n 5000 1.0875 1.0875 12000000.0875n 2801.0875 1 87n 3671.087587n 367log 1.0875 log 87n 367log 1.0875 log87n 367log87log 1.0875n17.16056585n 18n 5000 1.0875 1.0875 12000000.0875n 2801.0875 1 87n 3671.087587n 367log 1.0875 log 87n 367log 1.0875 log87n 367log87log 1.0875n17.16056585n 18n Thus 2021 is the first year when the fund exceeds $200000d*) What annual instalment would have produced $1000000 by 31st December 2020?d*) What annual instalment would have produced $1000000 by 31st December 2020? 18 17Amount 1.0875 1.0875 1.0875P P P d*) What annual instalment would have produced $1000000 by 31st December 2020? 18 17Amount 1.0875 1.0875 1.0875P P P 1.0875 , 1.0875, 18a P r n d*) What annual instalment would have produced $1000000 by 31st December 2020? 18 17Amount 1.0875 1.0875 1.0875P P P 1.0875 , 1.0875, 18a P r n 18i.e. 1000000S d*) What annual instalment would have produced $1000000 by 31st December 2020? 18 17Amount 1.0875 1.0875 1.0875P P P 1.0875 , 1.0875, 18a P r n 18i.e. 1000000S 181.0875 1.0875 110000000.0875P d*) What annual instalment would have produced $1000000 by 31st December 2020? 18 17Amount 1.0875 1.0875 1.0875P P P 1.0875 , 1.0875, 18a P r n 18i.e. 1000000S 181.0875 1.0875 110000000.0875P 181000000 0.08751.0875 1.0875 1P d*) What annual instalment would have produced $1000000 by 31st December 2020? 18 17Amount 1.0875 1.0875 1.0875P P P 1.0875 , 1.0875, 18a P r n 18i.e. 1000000S 181.0875 1.0875 110000000.0875P 181000000 0.08751.0875 1.0875 1P 22818.16829d*) What annual instalment would have produced $1000000 by 31st December 2020? 18 17Amount 1.0875 1.0875 1.0875P P P 1.0875 , 1.0875, 18a P r n 18i.e. 1000000S 181.0875 1.0875 110000000.0875P 181000000 0.08751.0875 1.0875 1P 22818.16829An annual instalment of $22818.17 will produce $1000000Loan RepaymentsLoan RepaymentsThe amount still owing after n time periods is; Loan Repayments principal plus interest instalments plus interestnA The amount still owing after n time periods is; Loan Repayments principal plus interest instalments plus interestnA The amount still owing after n time periods is; e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an overseas holiday. Interest is charged at 12% p.a., compounded monthly. They start repaying the loan one month after taking it out, and their monthly instalments are $300.Loan Repayments principal plus interest instalments plus interestnA The amount still owing after n time periods is; e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an overseas holiday. Interest is charged at 12% p.a., compounded monthly. They start repaying the loan one month after taking it out, and their monthly instalments are $300.a) How much will they still owe the bank at the end of six years?Loan Repayments principal plus interest instalments plus interestnA The amount still owing after n time periods is; e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an overseas holiday. Interest is charged at 12% p.a., compounded monthly. They start repaying the loan one month after taking it out, and their monthly instalments are $300.a) How much will they still owe the bank at the end of six years?Initial loan is borrowed for 72 months 7220000 1.01Loan Repayments principal plus interest instalments plus interestnA The amount still owing after n time periods is; e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an overseas holiday. Interest is charged at 12% p.a., compounded monthly. They start repaying the loan one month after taking it out, and their monthly instalments are $300.a) How much will they still owe the bank at the end of six years?Initial loan is borrowed for 72 months 7220000 1.01Repayments are an investment in your loanLoan Repayments principal plus interest instalments plus interestnA The amount still owing after n time periods is; e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an overseas holiday. Interest is charged at 12% p.a., compounded monthly. They start repaying the loan one month after taking it out, and their monthly instalments are $300.a) How much will they still owe the bank at the end of six years? 71300 1.011st repayment invested for 71 monthsInitial loan is borrowed for 72 months 7220000 1.01Repayments are an investment in your loanLoan Repayments principal plus interest instalments plus interestnA The amount still owing after n time periods is; e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an overseas holiday. Interest is charged at 12% p.a., compounded monthly. They start repaying the loan one month after taking it out, and their monthly instalments are $300.a) How much will they still owe the bank at the end of six years? 71300 1.011st repayment invested for 71 monthsInitial loan is borrowed for 72 months 7220000 1.01 70300 1.012nd repayment invested for 70 monthsRepayments are an investment in your loanLoan Repayments principal plus interest instalments plus interestnA The amount still owing after n time periods is; e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an overseas holiday. Interest is charged at 12% p.a., compounded monthly. They start repaying the loan one month after taking it out, and their monthly instalments are $300.a) How much will they still owe the bank at the end of six years? 71300 1.011st repayment invested for 71 monthsInitial loan is borrowed for 72 months 7220000 1.01 70300 1.012nd repayment invested for 70 months 1300 1.012nd last repayment invested for 1 monthRepayments are an investment in your loanLoan Repayments principal plus interest instalments plus interestnA The amount still owing after n time periods is; e.g. (i) Richard and Kathy borrow $20000 from the bank to go on an overseas holiday. Interest is charged at 12% p.a., compounded monthly. They start repaying the loan one month after taking it out, and their monthly instalments are $300.a) How much will they still owe the bank at the end of six years? 71300 1.011st repayment invested for 71 monthsInitial loan is borrowed for 72 months 7220000 1.01 70300 1.012nd repayment invested for 70 months 1300 1.012nd last repayment invested for 1 month300last repayment invested for 0 monthsRepayments are an investment in your loan principal plus interest instalments plus interestnA principal plus interest instalments plus interestnA 72 70 7172 20000 1.01 300 300 1.01 300 1.01 300 1.01A principal plus interest instalments plus interestnA 72 70 7172 20000 1.01 300 300 1.01 300 1.01 300 1.01A 300, 1.01, 72a r n principal plus interest instalments plus interestnA 72 70 7172 20000 1.01 300 300 1.01 300 1.01 300 1.01A 300, 1.01, 72a r n 72 120000 1.011na rr principal plus interest instalments plus interestnA 72 70 7172 20000 1.01 300 300 1.01 300 1.01 300 1.01A 300, 1.01, 72a r n 72 120000 1.011na rr 7272 300 1.01 120000 1.010.01$9529.01 principal plus interest instalments plus interestnA 72 70 7172 20000 1.01 300 300 1.01 300 1.01 300 1.01A 300, 1.01, 72a r n 72 120000 1.011na rr 7272 300 1.01 120000 1.010.01$9529.01b) How much interest will they have paid in six years? principal plus interest instalments plus interestnA 72 70 7172 20000 1.01 300 300 1.01 300 1.01 300 1.01A 300, 1.01, 72a r n 72 120000 1.011na rr 7272 300 1.01 120000 1.010.01$9529.01b) How much interest will they have paid in six years?Total repayments = 300 72$21600 principal plus interest instalments plus interestnA 72 70 7172 20000 1.01 300 300 1.01 300 1.01 300 1.01A 300, 1.01, 72a r n 72 120000 1.011na rr 7272 300 1.01 120000 1.010.01$9529.01b) How much interest will they have paid in six years?Total repayments = 300 72$21600Loan reduction = 20000 9529.01$10470.99 principal plus interest instalments plus interestnA 72 70 7172 20000 1.01 300 300 1.01 300 1.01 300 1.01A 300, 1.01, 72a r n 72 120000 1.011na rr 7272 300 1.01 120000 1.010.01$9529.01b) How much interest will they have paid in six years?Total repayments = 300 72$21600Loan reduction = 20000 9529.01$10470.99= 21600 10470.99Interest $11129.01(ii) Finding the amount of each instalment(ii) Finding the amount of each instalmentYog borrows $30000 to buy a car. He will repay the loan in five years, paying 60 equal monthly instalments, beginning one month after he takes out the loan. Interest is charged at 9% p.a. compounded monthly.Find how much the monthly instalment shold be. (ii) Finding the amount of each instalmentYog borrows $30000 to buy a car. He will repay the loan in five years, paying 60 equal monthly instalments, beginning one month after he takes out the loan. Interest is charged at 9% p.a. compounded monthly.Find how much the monthly instalment shold be. Let the monthly instalment be $M(ii) Finding the amount of each instalmentYog borrows $30000 to buy a car. He will repay the loan in five years, paying 60 equal monthly instalments, beginning one month after he takes out the loan. Interest is charged at 9% p.a. compounded monthly.Find how much the monthly instalment shold be. Initial loan is borrowed for 60 months 6030000 1.0075Let the monthly instalment be $M(ii) Finding the amount of each instalmentYog borrows $30000 to buy a car. He will repay the loan in five years, paying 60 equal monthly instalments, beginning one month after he takes out the loan. Interest is charged at 9% p.a. compounded monthly.Find how much the monthly instalment shold be. Initial loan is borrowed for 60 months 6030000 1.0075 591.0075M1st repayment invested for 59 monthsLet the monthly instalment be $M(ii) Finding the amount of each instalmentYog borrows $30000 to buy a car. He will repay the loan in five years, paying 60 equal monthly instalments, beginning one month after he takes out the loan. Interest is charged at 9% p.a. compounded monthly.Find how much the monthly instalment shold be. Initial loan is borrowed for 60 months 6030000 1.0075 591.0075M1st repayment invested for 59 months 581.0075M2nd repayment invested for 58 monthsLet the monthly instalment be $M(ii) Finding the amount of each instalmentYog borrows $30000 to buy a car. He will repay the loan in five years, paying 60 equal monthly instalments, beginning one month after he takes out the loan. Interest is charged at 9% p.a. compounded monthly.Find how much the monthly instalment shold be. Initial loan is borrowed for 60 months 6030000 1.0075 591.0075M1st repayment invested for 59 months 581.0075M2nd repayment invested for 58 months 11.0075M2nd last repayment invested for 1 monthLet the monthly instalment be $M(ii) Finding the amount of each instalmentYog borrows $30000 to buy a car. He will repay the loan in five years, paying 60 equal monthly instalments, beginning one month after he takes out the loan. Interest is charged at 9% p.a. compounded monthly.Find how much the monthly instalment shold be. Initial loan is borrowed for 60 months 6030000 1.0075 591.0075M1st repayment invested for 59 months 581.0075M2nd repayment invested for 58 months 11.0075M2nd last repayment invested for 1 monthMlast repayment invested for 0 monthsLet the monthly instalment be $M principal plus interest instalments plus interestnA principal plus interest instalments plus interestnA 60 58 5960 30000 1.0075 1.0075 1.0075 1.0075A M M M M principal plus interest instalments plus interestnA 60 58 5960 30000 1.0075 1.0075 1.0075 1.0075A M M M M , 1.0075, 60a M r n principal plus interest instalments plus interestnA 60 58 5960 30000 1.0075 1.0075 1.0075 1.0075A M M M M , 1.0075, 60a M r n 60 130000 1.00751na rr principal plus interest instalments plus interestnA 60 58 5960 30000 1.0075 1.0075 1.0075 1.0075A M M M M , 1.0075, 60a M r n 60 130000 1.00751na rr 6060 1.0075 130000 1.00750.0075M principal plus interest instalments plus interestnA 60 58 5960 30000 1.0075 1.0075 1.0075 1.0075A M M M M , 1.0075, 60a M r n 60 130000 1.00751na rr 6060 1.0075 130000 1.00750.0075M 60But 0A principal plus interest instalments plus interestnA 60 58 5960 30000 1.0075 1.0075 1.0075 1.0075A M M M M , 1.0075, 60a M r n 60 130000 1.00751na rr 6060 1.0075 130000 1.00750.0075M 60But 0A 6060 1.0075 130000 1.0075 00.0075M principal plus interest instalments plus interestnA 60 58 5960 30000 1.0075 1.0075 1.0075 1.0075A M M M M , 1.0075, 60a M r n 60 130000 1.00751na rr 6060 1.0075 130000 1.00750.0075M 60But 0A 6060 1.0075 130000 1.0075 00.0075M 60601.0075 1 30000 1.00750.0075M principal plus interest instalments plus interestnA 60 58 5960 30000 1.0075 1.0075 1.0075 1.0075A M M M M , 1.0075, 60a M r n 60 130000 1.00751na rr 6060 1.0075 130000 1.00750.0075M 60But 0A 6060 1.0075 130000 1.0075 00.0075M 60601.0075 1 30000 1.00750.0075M 606030000 1.0075 0.00751.0075 1M principal plus interest instalments plus interestnA 60 58 5960 30000 1.0075 1.0075 1.0075 1.0075A M M M M , 1.0075, 60a M r n 60 130000 1.00751na rr 6060 1.0075 130000 1.00750.0075M 60But 0A 6060 1.0075 130000 1.0075 00.0075M 60601.0075 1 30000 1.00750.0075M 606030000 1.0075 0.00751.0075 1M $622.75M (iii) Finding the length of the loan(iii) Finding the length of the loan2005 HSC Question 8c)Weelabarrabak Shire Council borrowed $3000000 at the beginning of 2005. The annual interest rate is 12%. Each year, interest is calculated on the balance at the beginning of the year and added to the balance owing. The debt is to be repaid by equal annual repayments of $480000, with the first repayment being made at the end of 2005. Let be the balance owing after the th repayment.nA n(iii) Finding the length of the loan2005 HSC Question 8c)Weelabarrabak Shire Council borrowed $3000000 at the beginning of 2005. The annual interest rate is 12%. Each year, interest is calculated on the balance at the beginning of the year and added to the balance owing. The debt is to be repaid by equal annual repayments of $480000, with the first repayment being made at the end of 2005. Let be the balance owing after the th repayment.nA n 26 52(i) Show that 3 10 1.12 4.8 10 1 1.12A (iii) Finding the length of the loan2005 HSC Question 8c)Weelabarrabak Shire Council borrowed $3000000 at the beginning of 2005. The annual interest rate is 12%. Each year, interest is calculated on the balance at the beginning of the year and added to the balance owing. The debt is to be repaid by equal annual repayments of $480000, with the first repayment being made at the end of 2005. Let be the balance owing after the th repayment.nA n 26 52(i) Show that 3 10 1.12 4.8 10 1 1.12A Initial loan is borrowed for 2 years 23000000 1.12(iii) Finding the length of the loan2005 HSC Question 8c)Weelabarrabak Shire Council borrowed $3000000 at the beginning of 2005. The annual interest rate is 12%. Each year, interest is calculated on the balance at the beginning of the year and added to the balance owing. The debt is to be repaid by equal annual repayments of $480000, with the first repayment being made at the end of 2005. Let be the balance owing after the th repayment.nA n 26 52(i) Show that 3 10 1.12 4.8 10 1 1.12A Initial loan is borrowed for 2 years 23000000 1.12 1480000 1.121st repayment invested for 1 year(iii) Finding the length of the loan2005 HSC Question 8c)Weelabarrabak Shire Council borrowed $3000000 at the beginning of 2005. The annual interest rate is 12%. Each year, interest is calculated on the balance at the beginning of the year and added to the balance owing. The debt is to be repaid by equal annual repayments of $480000, with the first repayment being made at the end of 2005. Let be the balance owing after the th repayment.nA n 26 52(i) Show that 3 10 1.12 4.8 10 1 1.12A Initial loan is borrowed for 2 years 23000000 1.12 1480000 1.121st repayment invested for 1 year4800002nd repayment invested for 0 years(iii) Finding the length of the loan2005 HSC Question 8c)Weelabarrabak Shire Council borrowed $3000000 at the beginning of 2005. The annual interest rate is 12%. Each year, interest is calculated on the balance at the beginning of the year and added to the balance owing. The debt is to be repaid by equal annual repayments of $480000, with the first repayment being made at the end of 2005. Let be the balance owing after the th repayment.nA n 26 52(i) Show that 3 10 1.12 4.8 10 1 1.12A Initial loan is borrowed for 2 years 23000000 1.12 1480000 1.121st repayment invested for 1 year4800002nd repayment invested for 0 years principal plus interest instalments plus interestnA (iii) Finding the length of the loan2005 HSC Question 8c)Weelabarrabak Shire Council borrowed $3000000 at the beginning of 2005. The annual interest rate is 12%. Each year, interest is calculated on the balance at the beginning of the year and added to the balance owing. The debt is to be repaid by equal annual repayments of $480000, with the first repayment being made at the end of 2005. Let be the balance owing after the th repayment.nA n 26 52(i) Show that 3 10 1.12 4.8 10 1 1.12A Initial loan is borrowed for 2 years 23000000 1.12 1480000 1.121st repayment invested for 1 year4800002nd repayment invested for 0 years principal plus interest instalments plus interestnA 22 3000000 1.12 480000 480000 1.12A (iii) Finding the length of the loan2005 HSC Question 8c)Weelabarrabak Shire Council borrowed $3000000 at the beginning of 2005. The annual interest rate is 12%. Each year, interest is calculated on the balance at the beginning of the year and added to the balance owing. The debt is to be repaid by equal annual repayments of $480000, with the first repayment being made at the end of 2005. Let be the balance owing after the th repayment.nA n 26 52(i) Show that 3 10 1.12 4.8 10 1 1.12A Initial loan is borrowed for 2 years 23000000 1.12 1480000 1.121st repayment invested for 1 year4800002nd repayment invested for 0 years principal plus interest instalments plus interestnA 22 3000000 1.12 480000 480000 1.12A 26 52 3 10 1.12 4.8 10 1 1.12A 6(ii) Show that 10 4 1.12 nnA 6(ii) Show that 10 4 1.12 nnA Initial loan is borrowed for n years 3000000 1.12 n 6(ii) Show that 10 4 1.12 nnA Initial loan is borrowed for n years 3000000 1.12 n 1480000 1.12 n1st repayment invested for n 1 years 6(ii) Show that 10 4 1.12 nnA Initial loan is borrowed for n years 3000000 1.12 n 1480000 1.12 n1st repayment invested for n 1 years 2480000 1.12 n2nd repayment invested for n 2 years 6(ii) Show that 10 4 1.12 nnA Initial loan is borrowed for n years 3000000 1.12 n 1480000 1.12 n1st repayment invested for n 1 years 2480000 1.12 n2nd repayment invested for n 2 years 1480000 1.122nd last repayment invested for 1 year 6(ii) Show that 10 4 1.12 nnA Initial loan is borrowed for n years 3000000 1.12 n 1480000 1.12 n1st repayment invested for n 1 years 2480000 1.12 n2nd repayment invested for n 2 years 1480000 1.122nd last repayment invested for 1 year480000last repayment invested for 0 years 6(ii) Show that 10 4 1.12 nnA Initial loan is borrowed for n years 3000000 1.12 n 1480000 1.12 n1st repayment invested for n 1 years 2480000 1.12 n2nd repayment invested for n 2 years 1480000 1.122nd last repayment invested for 1 year480000last repayment invested for 0 years principal plus interest instalments plus interestnA 6(ii) Show that 10 4 1.12 nnA Initial loan is borrowed for n years 3000000 1.12 n 1480000 1.12 n1st repayment invested for n 1 years 2480000 1.12 n2nd repayment invested for n 2 years 1480000 1.122nd last repayment invested for 1 year480000last repayment invested for 0 years principal plus interest instalments plus interestnA 2 13000000 1.12 480000 1 1.12 1.12 1.12n n nnA 6(ii) Show that 10 4 1.12 nnA Initial loan is borrowed for n years 3000000 1.12 n 1480000 1.12 n1st repayment invested for n 1 years 2480000 1.12 n2nd repayment invested for n 2 years 1480000 1.122nd last repayment invested for 1 year480000last repayment invested for 0 years principal plus interest instalments plus interestnA 2 13000000 1.12 480000 1 1.12 1.12 1.12n n nnA 480000, 1.12,a r n n 6(ii) Show that 10 4 1.12 nnA Initial loan is borrowed for n years 3000000 1.12 n 1480000 1.12 n1st repayment invested for n 1 years 2480000 1.12 n2nd repayment invested for n 2 years 1480000 1.122nd last repayment invested for 1 year480000last repayment invested for 0 years principal plus interest instalments plus interestnA 2 13000000 1.12 480000 1 1.12 1.12 1.12n n nnA 480000, 1.12,a r n n 13000000 1.121nn a rr 480000 1.12 13000000 1.120.12nnnA 480000 1.12 13000000 1.120.12nnnA 3000000 1.12 4000000 1.12 1n n 480000 1.12 13000000 1.120.12nnnA 3000000 1.12 4000000 1.12 1n n 3000000 1.12 4000000 1.12 4000000n n 480000 1.12 13000000 1.120.12nnnA 3000000 1.12 4000000 1.12 1n n 3000000 1.12 4000000 1.12 4000000n n 4000000 1000000 1.12 n 480000 1.12 13000000 1.120.12nnnA 3000000 1.12 4000000 1.12 1n n 3000000 1.12 4000000 1.12 4000000n n 4000000 1000000 1.12 n 610 4 1.12 n 480000 1.12 13000000 1.120.12nnnA 3000000 1.12 4000000 1.12 1n n 3000000 1.12 4000000 1.12 4000000n n 4000000 1000000 1.12 n 610 4 1.12 n (iii) In which year will Weelabarrabak Shire Council make the final repayment? 480000 1.12 13000000 1.120.12nnnA 3000000 1.12 4000000 1.12 1n n 3000000 1.12 4000000 1.12 4000000n n 4000000 1000000 1.12 n 610 4 1.12 n (iii) In which year will Weelabarrabak Shire Council make the final repayment?0nA 480000 1.12 13000000 1.120.12nnnA 3000000 1.12 4000000 1.12 1n n 3000000 1.12 4000000 1.12 4000000n n 4000000 1000000 1.12 n 610 4 1.12 n (iii) In which year will Weelabarrabak Shire Council make the final repayment?0nA 610 4 1.12 0n 480000 1.12 13000000 1.120.12nnnA 3000000 1.12 4000000 1.12 1n n 3000000 1.12 4000000 1.12 4000000n n 4000000 1000000 1.12 n 610 4 1.12 n (iii) In which year will Weelabarrabak Shire Council make the final repayment?0nA 610 4 1.12 0n 4 1.12 0n 480000 1.12 13000000 1.120.12nnnA 3000000 1.12 4000000 1.12 1n n 3000000 1.12 4000000 1.12 4000000n n 4000000 1000000 1.12 n 610 4 1.12 n (iii) In which year will Weelabarrabak Shire Council make the final repayment?0nA 610 4 1.12 0n 4 1.12 0n 1.12 4n log 1.12 log 4n log 1.12 log 4n log1.12 log 4n log 1.12 log 4n log1.12 log 4n log 4log1.12n 12.2325075n log 1.12 log 4n log1.12 log 4n log 4log1.12n 12.2325075n The thirteenth repayment is the final repayment which will occur at the end of 2017 log 1.12 log 4n log1.12 log 4n log 4log1.12n 12.2325075n The thirteenth repayment is the final repayment which will occur at the end of 2017Exercise 7B; 4, 6, 8, 10Exercise 7C; 1, 4, 7, 9Exercise 7D; 3, 4, 9, 11Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38Slide Number 39Slide Number 40Slide Number 41Slide Number 42Slide Number 43Slide Number 44Slide Number 45Slide Number 46Slide Number 47Slide Number 48Slide Number 49Slide Number 50Slide Number 51Slide Number 52Slide Number 53Slide Number 54Slide Number 55Slide Number 56Slide Number 57Slide Number 58Slide Number 59Slide Number 60Slide Number 61Slide Number 62Slide Number 63Slide Number 64Slide Number 65Slide Number 66Slide Number 67Slide Number 68Slide Number 69Slide Number 70Slide Number 71Slide Number 72Slide Number 73Slide Number 74Slide Number 75Slide Number 76Slide Number 77Slide Number 78Slide Number 79Slide Number 80Slide Number 81Slide Number 82Slide Number 83Slide Number 84Slide Number 85Slide Number 86Slide Number 87Slide Number 88Slide Number 89Slide Number 90Slide Number 91Slide Number 92Slide Number 93Slide Number 94Slide Number 95Slide Number 96Slide Number 97Slide Number 98Slide Number 99Slide Number 100Slide Number 101Slide Number 102Slide Number 103Slide Number 104Slide Number 105Slide Number 106Slide Number 107Slide Number 108Slide Number 109Slide Number 110Slide Number 111Slide Number 112Slide Number 113Slide Number 114Slide Number 115Slide Number 116Slide Number 117Slide Number 118Slide Number 119Slide Number 120Slide Number 121Slide Number 122Slide Number 123Slide Number 124Slide Number 125Slide Number 126Slide Number 127Slide Number 128Slide Number 129Slide Number 130