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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

Respuesta :

In general, the compound interest formula is

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

In our case,

[tex]A=40000,r=4\%=0.04,n=2,t=7[/tex]

Therefore,

[tex]\Rightarrow40000=P(1+\frac{0.04}{2})^{14}[/tex]

Solving for P,

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

The answer is approximately $30315

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