Time Value of Money

Elementary level Finance

Present Value

A little Babie Duckie plans to buy a $225 rotisserie oven to roast itself in 5 years when it grows up. If a bank offers 7.5% annually compounded interest, how much money does the Duckie have to invest now in order to afford the rotisserie oven 5 years later?

This amount is called the Present Value:• The value of the money as of today.

Future Value

If the little Babie Duckie only has $140 today, and the bank offers 7.5% annually compounded interest. How much money will the little Babie Duckie have after 5 years?

This amount is called the Future Value:• The value of the money at a future time t

years from today.

Annuity

An Annuity is a series of payments made at specified times.

Example: depositing $100 into a bank with 5% interest every year for 10 years.

Example: Present Value of an Annuity

A farmer wants to buy a piece of land to rear ducks to roast. The farmer agrees to make annual payments of $2500 for 15 years, with the first payment starting a year from now. If the interest rate is 6%, find the present value of the piece of land.

Example:Future Value of an annuity

A little Babie Duckie, starting this year, decides to invest in a life insurance to secure its life. The Duckie deposits 50$ at the end of each year for 8 years with an annual interest rate of 5%. Find the future value of this insurance after 8 years.

Investment

Assume that you are 16 this year, and are planning to retire as a millionaire at 66 by investing a little bit of money at the end of every year in a bank account with 6% annual interest. How much should you invest each year?

What if you wait until 10 years later to start your investment?

Example

A house is valued at $300,000 today. If the house can be purchased with 30 equal annual payments at the end of each year, at an interest rate of 6%, find the amount of each payment.

Perpetuity:Infinite Annuity

A perpetuity is an annuity that has no definite end.

Example: Perpetuity

A retired teacher wants to establish a scholarship fund that pays 1200$ to one graduating senior with high aesthetic sense every year in the future. The interest rate is consistently set to be 6%. How much does the teacher have to donate in order to found the fund?

Example: Perpetuity

A Cactus has saved $20000. At the beginning of the year, it purchases a perpetuity with annual end-of-year payments. The perpetuity price is based on an annual interest rate of 5%. What are the annual payments for the Cactus’ perpetuity?

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