FV_Ex1FV Example 1: $5000 Initial Deposit & $200 per month Deposits4% Annual Interest, 18 Years, Compounded Monthly

Compounds:MonthlyYearly RateYearsMonthly PaymentsInitial Deposit (PV)TypeFuture Value

You wish to open a account for you newborns college in 18 years. You plan on making an initial deposit of $5,000 and making monthly deposits of $200. The account compounds monthly with a yearly rate of 4%.

How much will you have in 18 Years?

=FV(Rate,Total_Periods,Payments,PV,Type)

FV_Ex2FV Example 2: $100 Initial Deposit Only6% Annual Interest, 3 years, Compounds Semi-Annually.

Compounds:Yearly RateYearsPaymentsInitial Deposit (PV)TypeFuture Value

You are opening an account with $100. The account compounds semi-annually. At 6% yearly interest, what will you have in 3 years?

=FV(Rate,Total_Periods,Payments,PV,Type)

FV_Ex3FV Example 3: $5,000 Payments Only4% Annual Interest, 10 Years, Beg. Of Period

Compounds:YearlyYearly RateYearsPaymentsInitial Deposit (PV)TypeFuture Value

You are depositing $5,000 into an account yearly for the next 10 years at 4% annual interest. Interest is compounded yearly at the beginning of the period.

What is the Future Value?

=FV(Rate,Total_Periods,Payments,PV,Type)

Eff_Rate_Ex1

Nominal RatePeriods Per YearEffective Rate

=Effect(Nominal Rate,Number of Compounding Periods Per Year)

Effective Rate Example 1:Comparing Different Loan Rates We are looking for a credit card company that offers the best rate and have found three we wish to compare. The first has a nominal rate of 17% and compounds monthly, the second has a rate of 17.5% and compounds semi-annually (twice a year), and the third has a rate of 18% and compounds quarterly. Which one has the best effective rate? (i.e. the lowest?)

Eff_Rate_Ex2

Example 2: Payments & Compounding Periods Differ (5 Year Loan)Annual Rate:Number of Times Compounded per year:Life of Loan:Payments (Made Yearly):Type:

Rate Equivalent Using Effect()

Future Value:

Effective Rate Example 2:FV with Yearly Payments, Compounding Monthly We are making yearly payments of $1000 for 5 years into an account which compounds monthly. The annual nominal interest rate is 6%. The payments are made at the end of each year (regular annuity).

The number of payments per year must equal the number of compounding periods per year. Because Payments are made yearly, we need an equivalent rate which compounds yearly (i.e. the effective yearly rate)

=Effect(Nominal Rate, Periods Per Year)=FV(Rate,Total Periods,Payments,PV,Type)

Nominal_Rate

Payments & Compounding Periods Differ (5 Year Loan)Annual Rate:Number of Times Compounded per year:Life of Loan:Payments (Semi-Yearly):Type:

Effective Yrly Rate for an account compounding Monthly:Nominal Yrly Rate for an account compounding Semi-Annually:Future Value:

=Effect(Nominal Rate,Number of Compounding Periods Per Year)=Nominal(Effective Rate,Number of Compounding Periods Per Year)

We are making semi-yearly payments of $1000 into an account for 5 years. The account compounds monthly. The annual nominal interest rate is 4%. The payments are made at the end of each period (regular annuity). Find the Future Value.

The number of payments we are making per year must equal the number of compounding periods per year.Step 1: First, we will find the Effective yearly rate equilavent of an account which compounds monthly.Step 2: Now that we have the effective yearly rate, we use nominal() to convert it into the nominal rate for an account which compounds semi-annually.

PV_Ex1ScenarioOption AOption BOption CYearly Rate:Years:Payments:Future Value:Type:Present Value:

You are loaning an associate $1,000. For repayment options, the suggest the scenarios below. The going market rate is 4% compounded monthly. Which option should you take? Assume risk is the same for all three options.

OPTION A:Will pay you $1,200 after 1 year.OPTION B:Will pay you $1,400 at the end of 2 years.OPTION C:Will pay you $100 per month for 12 months then $150.

PV_Ex2Bond Cash Flow Discounting Example - PV()Face Value:Years to Maturity:Coupon Rate:Present Value (Purchase Price):Discount Rate Used for Valuation:Yearly Coupon Payments:Present Value: (Includes Coupon Payments + Face Value)Discounted Profit: (Present Value - Purchase Price)

Bond Cash Flow Discounting Example PV()We have purchased a 3 year bond with a face value of $1,000 for $961.15. Its coupon rate is 6% resulting in yearly payments of $60 (face value x coupon rate). The market is currently paying about 5% for investments of equal risk. What is the Bond's Present Value?

=PV(Rate,#periods,CouponPayment,FaceValue)

PMT_Ex1PMT Example 1: Loan PaymentsRate:Years:Present ValueFuture ValueType

Monthly Payments:PeriodPrincipleInterestBalance

PMT() Example 1 - You are planning to buy a new car. You are taking out a 5 year loan of $20,000 to help you pay for it and you are borrowing at a yearly interest rate of 6%. What will the monthly loan payments be?

=PMT(Rate,Total#ofPeriods,PV,FV,Type)

PMT_Ex2PMT Example 2: Retirement Goal Using Effective RateNominal Rate:Effective Rate:Years:Present ValueFuture ValueType

Yearly Payments:

PMT() Example 2: - You would like to have $1,000,000 in your savings account by the time you retire. You have 30 years until retirement and you have found a CD account which pays 5.5% annual interest. You plan on making yearly payments into an account which compounds monthly. How much do you have to deposit each year to reach your goal?

=PMT(Rate,Total#ofPeriods,PV,FV,Type)=Effect(Nominal Rate,Compounding Periods)

Payments_Array

Nper()RatePaymentsPresent ValueFuture ValueTypeNumber of Periods:Number of Years:Today's Date:Target Date:

=NPER(Rate,Payments,PV,FV,Type)You are planning on making montlhly deposits of $100 into a savings account which compounds monthly with a yearly rate of 4%. How many years will it take you to have $25,000?What will the date be? (From the current date?)

Rate_Ex1Rate Example 1: Return on your Investment: Single PaymentPresent Value:Periods (In Years):Payments:Future Value:Yearly Rate on Investment (Cmp Yearly):Yearly Rate on Investment (Cmp Monthly):

Rate() Example 15 Years ago you purchased a 1969 Ford Falcon for $5,000. You sold it today for $12,000.

What yearly return did you get on your investment if compounding yearly?Whay yearly return did you get on your inventment if compounding is monthly?

Rate(#periods,Payments,PresentValue,FutureValue,Type,Guess)

Rate_Ex2Rate Example 2: Return on your Inventment - Multiple PaymentsPurchase Price (PV)Compounding Periods:Payments:Future Value:Yearly Rate

You are investing in an annuity that requires you to deposit $50 at the end of every 6 months for 2 years (i.e. total of 4 payments). At the end of the 2 years you will receive a payment of $209,18.

What Yearly Rate are you getting?

NPV()NPV Example 1 - Investment Made TodayNPV Example 2 - Investment Made in One YearAnnual Rate:Annual Rate:

YearAmountYearAmount11223344556Present Value:Net Present Value:Net Present Value:

NPV() Cash Flows VaryYou are considering an investment opportunity that will cost you $3,000 and pay the following amounts at the end of each year for the following 5 years: $500, $600, $700, $900, and $850. The going interest rate of investments of similar risk is 6%. Should you make the investment?

IRR()

IRR Example 1

YearAmount012345

Internal Rate of Return:

Internal Rate of Return: =IRR(Values,Guess)

You are investing 3K and will receive the following payment at the end of each year: 500, 600, 700, 900, & 850.- Cash flows must occur at regular periods.- The amount of the cash flows do not have to be identical as they would be for an annuity.- IRR uses the order of values to interpret the order of cash flows. Be sure to enter your payment and income values in the sequence they occur.- The initial flow is the investment and must be negative. Subsequent flows should be positive. If in one of your years you have a negative cash flow, you cannot use Excel's IRR function. A negative cash flow produces and second IRR and Excel only displays a single value for IRR. Use MIRR instead.Note that IRR assumes cash generated during the investment is reinvested at the rate calculated by IRR. This can overstate IRR for investments which generate a lot of cash over the life of the investment.

MIRR()

MIRR Example 2: Single InvestmentInvestmentYear 1Year 2Year 3Year 4Year 5Year 6Year 7Finance Rate:Reinvest Rate:

MIRR

Modified Internal Rate of Return: =MIRR(Values,FinanceRate,ReinventRate) IRR assumes that the rate you finance your investment is the same as the rate you reinent your profits. Further, it cannot have any negative cash flows after the initial inventment. MIRR addresses both of these issues.

You are investing 200K to purchase an oil well and will receive the cash flows shown below. In the final year, you will incur a cost of $30K for hazardous waste clean up. Profits are reinvented at 5% and the 30K is financed at 6%.

FinancialsPERMNODateCompanyNameExchangeTickerSymbolPriceorBid/AskAverageClosing BidGroup1459312/28/10APPLE INCAAPL$325.47$325.47Electronics1459312/29/10APPLE INCAAPL$325.29$325.17Electronics1459312/22/10APPLE INCAAPL$325.16$325.15Electronics1459312/27/10APPLE INCAAPL$324.68$324.73Electronics1459312/21/10APPLE INCAAPL$324.20$324.19Electronics1459312/30/10APPLE INCAAPL$323.66$323.65Electronics1459312/23/10APPLE INCAAPL$323.60$323.51Electronics1459312/31/10APPLE INCAAPL$322.56$322.48Electronics1459312/20/10APPLE INCAAPL$322.21$322.19Electronics1459312/13/10APPLE INCAAPL$321.67$321.60Electronics1459312/16/10APPLE INCAAPL$321.25$321.02Electronics1459312/8/10APPLE INCAAPL$321.01$320.92Electronics1459312/17/10APPLE INCAAPL$320.61$320.61Electronics1459312/10/10APPLE INCAAPL$320.56$320.44Electronics1459312/15/10APPLE INCAAPL$320.36$320.40Electronics1459312/14/10APPLE INCAAPL$320.29$320.25Electronics1459312/6/10APPLE INCAAPL$320.15$320.06Electronics1459312/9/10APPLE INCAAPL$319.76$319.84Electronics1459311/8/10APPLE INCAAPL$318.62$318.79Electronics1459312/7/10APPLE INCAAPL$318.21$318.20Electronics1459312/2/10APPLE INCAAPL$318.15$317.98Electronics1459311/10/10APPLE INCAAPL$318.03$317.95Electronics1459310/18/10APPLE INCAAPL$318.00$317.90Electronics1459311/4/10APPLE INCAAPL$318.27$317.79Electronics1459312/3/10APPLE INCAAPL$317.44$317.40Electronics1459311/5/10APPLE INCAAPL$317.13$317.05Electronics1459311/29/10APPLE INCAAPL$316.87$316.83Electronics1459311/11/10APPLE INCAAPL$316.66$316.53Electronics1459312/1/10APPLE INCAAPL$316.40$316.38Electronics1459311/9/10APPLE INCAAPL$316.08$315.73Electronics1459311/26/10APPLE INCAAPL$315.76$315.67Electronics1459310/15/10APPLE INCAAPL$314.74$314.95Electronics1459311/24/10APPLE INCAAPL$314.80$314.77Electronics1459311/22/10APPLE INCAAPL$313.36$313.34Electronics1459311/3/10APPLE INCAAPL$312.80$312.79Electronics1459311/30/10APPLE INCAAPL$311.15$311.01Electronics1459310/20/10APPLE INCAAPL$310.53$310.19Electronics1459310/21/10APPLE INCAAPL$309.52$309.49Electronics1459310/19/10APPLE INCAAPL$309.49$309.47Electronics1459311/2/10APPLE INCAAPL$309.36$309.38Electronics1459311/23/10APPLE INCAAPL$308.73$309.03Electronics1459310/25/10APPLE INCAAPL$308.84$308.83Electronics1459311/18/10APPLE INCAAPL$308.43$308.14Electronics1459310/26/10APPLE INCAAPL$308.05$308.05Electronics1459311/12/10APPLE INCAAPL$308.03$307.92Electronics1459310/22/10APPLE INCAAPL$307.47$307.80Electronics1459310/27/10APPLE INCAAPL$307.83$307.72Electronics1459311/15/10APPLE INCAAPL$307.04$307.17Electronics1459311/19/10APPLE INCAAPL$306.73$306.70Electronics1459310/28/10APPLE INCAAPL$305.24$305.17Electronics1459311/1/10APPLE INCAAPL$304.18$303.97Electronics1459310/14/10APPLE INCAAPL$302.31$302.24Electronics1459311/16/10APPLE INCAAPL$301.59$301.28Electronics1459310/29/10APPLE INCAAPL$300.98$300.88Electronics1459311/17/10APPLE INCAAPL$300.50$300.37Electronics1459310/13/10APPLE INCAAPL$300.14$300.20Electronics1459310/12/10APPLE INCAAPL$298.54$298.58Electronics1459310/11/10APPLE INCAAPL$295.36$295.36Electronics1459310/8/10APPLE INCAAPL$294.07$293.98Electronics145939/24/10APPLE INCAAPL$292.32$292.31Electronics145939/27/10APPLE INCAAPL$291.16$291.05Electronics1459310/7/10APPLE INCAAPL$289.22$289.10Electronics1459310/5/10APPLE INCAAPL$288.94$289.10Electronics1459310/6/10APPLE INCAAPL$289.19$288.85Electronics145939/23/10APPLE INCAAPL$288.92$288.80Electronics145939/22/10APPLE INCAAPL$287.75$287.69Electronics145939/29/10APPLE INCAAPL$287.37$287.33Electronics145939/28/10APPLE INCAAPL$286.86$286.78Electronics145939/21/10APPLE INCAAPL$283.77$284.14Electronics145939/30/10APPLE INCAAPL$283.75$283.75Electronics145939/20/10APPLE INCAAPL$283.23$283.31Electronics1459310/1/10APPLE INCAAPL$282.52$282.52Electronics1459310/4/10APPLE INCAAPL$278.64$278.60Electronics145939/16/10APPLE INCAAPL$276.57$276.57Electronics145939/17/10APPLE INCAAPL$275.37$275.27Electronics145936/18/10APPLE INCAAPL$274.07$274.06Electronics145936/22/10APPLE INCAAPL$273.85$273.45Electronics145936/17/10APPLE INCAAPL$271.87$271.81Electronics145936/23/10APPLE INCAAPL$270.97$270.88Electronics145934/23/10APPLE INCAAPL$270.83$270.86Electronics145936/21/10APPLE INCAAPL$270.17$270.30Electronics145939/15/10APPLE INCAAPL$270.22$270.29Electronics145934/26/10APPLE INCAAPL$269.50$269.48Electronics145936/24/10APPLE INCAAPL$269.00$268.73Electronics145934/29/10APPLE INCAAPL$268.64$268.57Electronics145936/28/10APPLE INCAAPL$268.30$268.29Electronics145939/14/10APPLE INCAAPL$268.06$267.91Electronics145936/16/10APPLE INCAAPL$267.25$267.25Electronics145939/13/10APPLE INCAAPL$267.04$267.18Electronics145934/22/10APPLE INCAAPL$266.47$266.36Electronics145935/3/10APPLE INCAAPL$266.35$266.35Electronics145936/25/10APPLE INCAAPL$266.70$265.98Electronics145937/27/10APPLE INCAAPL$264.08$264.05Electronics145936/2/10APPLE INCAAPL$263.95$263.78Electronics145939/10/10APPLE INCAAPL$263.41$263.39Electronics145936/3/10APPLE INCAAPL$263.12$263.38Electronics145939/9/10APPLE INCAAPL$263.07$263.07Electronics145938/4/10APPLE INCAAPL$262.98$262.87Electronics145939/8/10APPLE INCAAPL$262.92$262.79Electronics145934/27/10APPLE INCAAPL$262.04$262.23Electronics145935/12/10APPLE INCAAPL$262.09$262.06Electronics145938/3/10APPLE INCAAPL$261.93$261.91Electronics145938/2/10APPLE INCAAPL$261.85$261.76Electronics145938/9/10APPLE INCAAPL$261.75$261.73Electronics145938/5/10APPLE INCAAPL$261.70$261.64Electronics145934/28/10APPLE INCAAPL$261.60$261.60Electronics145934/30/10APPLE INCAAPL$261.09$261.00Electronics145937/28/10APPLE INCAAPL$260.96$260.98Electronics145936/1/10APPLE INCAAPL$260.83$260.79Electronics145937/23/10APPLE INCAAPL$259.94$260.01Electronics145938/6/10APPLE INCAAPL$260.09$260.00Electronics145936/15/10APPLE INCAAPL$259.69$259.69Electronics145937/9/10APPLE INCAAPL$259.62$259.62Electronics145938/10/10APPLE INCAAPL$259.41$259.31Electronics145937/26/10APPLE INCAAPL$259.28$259.27Electronics145937/22/10APPLE INCAAPL$259.02$259.27Electronics145934/21/10APPLE INCAAPL$259.22$259.22Electronics145939/3/10APPLE INCAAPL$258.77$258.75Electronics145937/7/10APPLE INCAAPL$258.67$258.73Electronics145935/4/10APPLE INCAAPL$258.68$258.59Electronics145937/29/10APPLE INCAAPL$258.11$258.11Electronics145935/13/10APPLE INCAAPL$258.36$258.07Electronics145937/8/10APPLE INCAAPL$258.09$258.07Electronics145939/7/10APPLE INCAAPL$257.81$257.84Electronics145937/12/10APPLE INCAAPL$257.29$257.26Electronics145935/28/10APPLE INCAAPL$256.88$257.16Electronics145937/30/10APPLE INCAAPL$257.25$257.15Electronics145935/11/10APPLE INCAAPL$256.52$256.35Electronics145936/29/10APPLE INCAAPL$256.17$256.35Electronics145935/5/10APPLE INCAAPL$255.99$256.11Electronics145936/4/10APPLE INCAAPL$255.97$255.96Electronics145937/21/10APPLE INCAAPL$254.24$254.25Electronics145936/14/10APPLE INCAAPL$254.28$254.05Electronics145935/17/10APPLE INCAAPL$254.22$254.04Electronics145935/10/10APPLE INCAAPL$253.99$253.89Electronics145935/14/10APPLE INCAAPL$253.82$253.86Electronics145935/27/10APPLE INCAAPL$253.35$253.49Electronics145936/11/10APPLE INCAAPL$253.51$253.47Electronics145938/18/10APPLE INCAAPL$253.07$253.05Electronics145937/14/10APPLE INCAAPL$252.73$252.83Electronics145935/18/10APPLE INCAAPL$252.36$252.24Electronics145939/2/10APPLE INCAAPL$252.17$252.03Electronics145937/13/10APPLE INCAAPL$251.80$252.00Electronics145937/20/10APPLE INCAAPL$251.89$251.99Electronics145938/17/10APPLE INCAAPL$251.97$251.83Electronics145938/12/10APPLE INCAAPL$251.79$251.74Electronics145936/30/10APPLE INCAAPL$251.53$251.48Electronics145937/15/10APPLE INCAAPL$251.45$251.21Electronics145936/7/10APPLE INCAAPL$250.94$251.02Electronics145936/10/10APPLE INCAAPL$250.51$250.74Electronics145939/1/10APPLE INCAAPL$250.33$250.29Electronics145938/11/10APPLE INCAAPL$250.19$250.07Electronics145937/16/10APPLE INCAAPL$249.90$249.94Electronics145938/19/10APPLE INCAAPL$249.88$249.88Electronics145938/20/10APPLE INCAAPL$249.64$249.62Electronics145936/8/10APPLE INCAAPL$249.33$249.35Electronics145938/13/10APPLE INCAAPL$249.10$249.10Electronics145934/15/10APPLE INCAAPL$248.92$248.92Electronics145937/6/10APPLE INCAAPL$248.63$248.61Electronics145937/1/10APPLE INCAAPL$248.48$248.46Electronics145935/19/10APPLE INCAAPL$248.34$248.30Electronics145938/16/10APPLE INCAAPL$247.64$247.63Electronics145934/16/10APPLE INCAAPL$247.40$247.35Electronics145934/19/10APPLE INCAAPL$247.07$246.97Electronics145937/2/10APPLE INCAAPL$246.94$246.82Electronics145935/24/10APPLE INCAAPL$246.76$246.76Electronics145935/6/10APPLE INCAAPL$246.25$246.02Electronics145938/23/10APPLE INCAAPL$245.80$245.69Electronics145934/14/10APPLE INCAAPL$245.69$245.62Electronics145937/19/10APPLE INCAAPL$245.58$245.52Electronics145935/25/10APPLE INCAAPL$245.22$245.19Electronics145934/20/10APPLE INCAAPL$244.59$244.60Electronics145935/26/10APPLE INCAAPL$244.11$244.05Electronics145936/9/10APPLE INCAAPL$243.20$243.20Electronics145938/31/10APPLE INCAAPL$243.10$243.20Electronics145938/25/10APPLE INCAAPL$242.89$242.74Electronics145938/30/10APPLE INCAAPL$242.50$242.51Electronics145934/13/10APPLE INCAAPL$242.43$242.39Electronics145935/21/10APPLE INCAAPL$242.32$242.32Electronics145934/12/10APPLE INCAAPL$242.29$242.22Electronics145934/9/10APPLE INCAAPL$241.79$241.86Electronics145938/27/10APPLE INCAAPL$241.62$241.50Electronics145934/7/10APPLE INCAAPL$240.60$240.58Electronics145938/26/10APPLE INCAAPL$240.28$240.28Electronics145938/24/10APPLE INCAAPL$239.93$240.18Electronics145934/8/10APPLE INCAAPL$239.95$239.90Electronics145934/6/10APPLE INCAAPL$239.54$239.53Electronics145934/5/10APPLE INCAAPL$238.49$238.48Electronics145935/20/10APPLE INCAAPL$237.76$237.39Electronics145934/1/10APPLE INCAAPL$235.97$235.94Electronics145933/30/10APPLE INCAAPL$235.85$235.83Electronics145935/7/10APPLE INCAAPL$235.86$235.62Electronics145933/31/10APPLE INCAAPL$235.00$234.91Electronics145933/29/10APPLE INCAAPL$232.39$232.31Electronics145933/26/10APPLE INCAAPL$230.90$230.90Electronics145933/24/10APPLE INCAAPL$229.37$229.37Electronics145933/23/10APPLE INCAAPL$228.36$228.38Electronics145933/12/10APPLE INCAAPL$226.60$226.61Electronics145933/25/10APPLE INCAAPL$226.65$226.55Electronics145933/11/10APPLE INCAAPL$225.50$225.46Electronics145933/10/10APPLE INCAAPL$224.84$224.84Electronics145933/22/10APPLE INCAAPL$224.75$224.79Electronics145933/18/10APPLE INCAAPL$224.65$224.72Electronics145933/16/10APPLE INCAAPL$224.45$224.53Electronics145933/17/10APPLE INCAAPL$224.12$224.02Electronics145933/15/10APPLE INCAAPL$223.84$223.82Electronics145933/9/10APPLE INCAAPL$223.02$223.02Electronics145933/19/10APPLE INCAAPL$222.25$222.13Electronics145933/8/10APPLE INCAAPL$219.08$218.99Electronics145933/5/10APPLE INCAAPL$218.95$218.97Electronics145931/19/10APPLE INCAAPL$215.04$215.01Electronics145931/5/10APPLE INCAAPL$214.38$214.35Electronics145931/4/10APPLE INCAAPL$214.01$214.23Electronics145931/8/10APPLE INCAAPL$211.98$211.96Electronics145931/20/10APPLE INCAAPL$211.73$211.69Electronics145931/6/10APPLE INCAAPL$210.97$210.93Electronics145931/13/10APPLE INCAAPL$210.65$210.67Electronics145933/4/10APPLE INCAAPL$210.71$210.64Electronics145931/7/10APPLE INCAAPL$210.58$210.54Electronics145931/11/10APPLE INCAAPL$210.11$210.02Electronics145933/3/10APPLE INCAAPL$209.33$209.24Electronics145931/14/10APPLE INCAAPL$209.43$209.22Electronics145933/1/10APPLE INCAAPL$208.99$209.02Electronics145933/2/10APPLE INCAAPL$208.85$208.62Electronics145931/21/10APPLE INCAAPL$208.07$207.93Electronics145931/27/10APPLE INCAAPL$207.88$207.86Electronics145931/12/10APPLE INCAAPL$207.72$207.72Electronics145931/15/10APPLE INCAAPL$205.93$205.91Electronics145931/26/10APPLE INCAAPL$205.94$205.88Electronics145932/26/10APPLE INCAAPL$204.62$204.62Electronics145932/16/10APPLE INCAAPL$203.40$203.40Electronics145932/18/10APPLE INCAAPL$202.93$203.03Electronics145931/25/10APPLE INCAAPL$203.08$202.86Electronics145932/17/10APPLE INCAAPL$202.55$202.46Electronics145932/25/10APPLE 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