Question

A couple plans to save for their child’s college education. What principle must be deposited by the parents when their child is born to have $43,000 when their child reaches the age of 18 assume the money earned 8% interest compounded quarterly round your answer to the nearest decimal

Answer 1

SOLUTION

We will apply the amount formula

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{Where } \\ A\text{ = amount = }43,000\text{ dollars } \\ P=pri\text{ncipal money deposited }=\text{ ?} \\ r=\text{interest rate = 8}\%=0.08 \\ n\text{ = number of times compounded = quarterly = 4} \\ t=\text{ time in years = 18years } \end{gathered}$

Substituting each into the equation, we have

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 43,000=P(1+\frac{0.08}{4})^{4\times18} \\ 43,000=P(1.02)^{72} \\ 43,000=4.161140375P \\ P=\frac{43,000}{4.161140375} \\ P=10,333.7056972 \end{gathered}$

Hence the answer is $10,333.71 to two decimal places