Question

Rene received an inheritance from his grandfather of $28,600. When he gets out of college in 2 years he wants to use it as a down payment on a house. If he puts all the money in a money market account paying 7.9% interest compounded semiannually, how much money will be in the account at the end of the two years to use as the down payment on the property?

Answer 1

hello

to solve this question, we need to use the formula of compound interest

$\begin{gathered} c\mathrm{}p=p(1+\frac{r}{n})^{nt} \\ c\mathrm{}p=\text{compound interest} \\ p=\text{ principal} \\ r=\text{rate} \\ n=\text{ number of times the interest is compounded} \\ t=\text{time} \end{gathered}$$\begin{gathered} c\mathrm{}p=p(1+\frac{r}{n})^{nt} \\ p=\text{ \ 28,600} \\ r=7.9\text{ \% =0.079} \\ t=2 \\ n=2 \end{gathered}$$\begin{gathered} c\mathrm{}p=28600(1+\frac{0.079}{2})^{2\times2} \\ c\mathrm{}p=28600(1+0.0395)^4 \\ c\mathrm{}p=28600\times1.0395^4 \\ c\mathrm{}p=28600\times1.1676 \\ c\mathrm{}p=33393.36 \end{gathered}$

from the calculation above, the money in the account after two years would be $33,393.36