Question

Part of Abernathy’s divorce settlement involves setting aside money today for college tuition for their daughter who enters college in 7 years. They estimate that the cost of four years’ tuition and fees at the state university their daughter will attend will be $40,000. Find the lump sum that must be invested at 4% compounded semiannually

Answer 1

In general, the compound interest formula is

$A=P(1+\frac{r}{n})^{nt}$

In our case,

$A=40000,r=4\%=0.04,n=2,t=7$

Therefore,

$\Rightarrow40000=P(1+\frac{0.04}{2})^{14}$

Solving for P,

$\begin{gathered} \Rightarrow P=\frac{40000}{(1+\frac{0.04}{2})^{14}}=30315.000983\ldots \\ \Rightarrow P\approx30315 \end{gathered}$

The answer is approximately $30315