Thelma is planning for her son's college education to begin five years from today. She estimates the yearly tuition, books, and living expenses to be $5,000 per year for a fourminusyear degree, assuming the expenses incur only at the end of the year. How much must Thelma deposit today, at an interest rate of 8 percent, for her son to be able to withdraw $5,000 per year for four years of college?

Atleast $13611.7 at 8% interest rate compounded anually

Explanation:

A=P(1+r/n)^nt

A: Total amout

P: Principal amount or amount to  be invested

r: interest rate

n: number of times interest is applied in a time period

t: total time period

Thlema must have atleast $20,000 after 5 years

20000=P×(1+ 0.08/1)^5

P= $ 13611.7

$16,560.63

Explanation:

To calculate this, the relevant formula to us the formula for calculating the present value of an ordinary annuity since the expenses is assumed to be incurred only at the end of the year. The formula is given as follows:

PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)

Where;

PV = Present value or the amount to deposit today?

P = yearly withdrawal = $5,000

r = interest rate = 8% = 0.08

n = number of years = 4

Substitute the values into equation (1) to have:

PV = 5,000 × [{1 - [1 ÷ (1+0.08)]^4} ÷ 0.08]

     = 5,000 × [{1 - [1 ÷ 1.08]^4} ÷ 0.08]

     = 5,000 × [{1 - [0.925925925925926]^4} ÷ 0.08]

     = 5,000 × [{1 - 0.735029852796453} ÷ 0.08]

     = 5,000 × [0.264970147203547 ÷ 0.08]

     = 5,000 × 3.31212684004434

PV = $16,560.63

Thelma must deposit $16,560.63 today.

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