Question

A couple plans to save for their child's college education. What principal must be deposited by the parents when their child is born in order to have $37,000 when the child reaches the age of 18? Assume the money earns 9% interest, compounded quarterly. (Round your answer to two decimal places.)

Answer 1

We can use the compound interest formula:

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

Where:

A = Amount = $37000

P = Principal

r = Interest rate = 9% = 0.09

n = Number of times interest is compounded per unit of time = 4 (Since it is compounded quarterly)

t = time = 18

Therefore:

`37000=P(1+(0.09)/(4))^(18*4)`

Solve for P:

`\begin{gathered} P=(37000)/(4.963165999) \\ P=7454.918 \end{gathered}`