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+(r)/(n))^(nt)`

In our case,

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

Therefore,

`\Rightarrow40000=P(1+(0.04)/(2))^(14)`

Solving for P,

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

The answer is approximately $30315