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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 :

We can use the compound interest formula:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

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:

[tex]37000=P(1+\frac{0.09}{4})^{18*4}[/tex]

Solve for P:

[tex]\begin{gathered} P=\frac{37000}{4.963165999} \\ P=7454.918 \end{gathered}[/tex]

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