# Alisha plans to attend university next year. Her grandmother wishes to deposit enough money today in an account paying 5.5% compounded annually so that she can make withdrawals of \$5,000 at the end of each year for 4 years. How much should her grandmother invest today?

The amount that Alisha's grandmother should invest is \$17,525.75. Alisha plans to attend university next year. Her grandmother wishes to deposit enough money today in an account paying 5.5% compounded annually so that she can make withdrawals of \$5,000 at the end of each year for 4 years. The amount that her grandmother has to invest today has to be determined.

This can be done using the concept of present value of money. If the rate of interest is r, the present value of an amount X after t years is equal to `X/(1+r)^t` .

An amount of \$5,000 is withdrawn at the end of the year for 4 years. The present value of these withdrawals is

`P = 5,000/(1+.055)^1 + 5,000/(1+.055)^2 + 5,000/(1+.055)^3+ 5,000/(1+.055)^4`

`P = 5,000*(1/(1+.055)^1 + 1/(1+.055)^2 + 1/(1+.055)^3+ 1/(1+.055)^4)`

`P = 5,000*3.5051`

P = 17,525.75.

Alisha's grandmother should invest \$17,525.75 today.

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