Question

If a savings account of $19,400 is compounded semiannually at 5,07% annual interest, how much will the account be worth in 32 months? Round your answer to thenearest cent, if necessary. Note: 365 days in a year and 30 days in a month.

Answer 1

From the question, we are provided with the following information:

$\begin{gathered} \text{Principal, P=\ 19,400} \\ \text{Rate, r=5.07\%} \\ r=\frac{5.07}{100}=0.0507 \\ \text{Time, t(in years)=}\frac{32}{12}=2.67years \\ N\text{umber of times interest applied per time period, n=2(semi-annually)} \end{gathered}$

The required parameter we are to find is the Amount, A.

Amount of a compound interest is given by the formula:

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

Thus, we have:

$\begin{gathered} A=19,400(1+\frac{0.0507}{2})^{2\times2.67} \\ A=19400(1+0.02535)^{5.34} \\ A=19400(1.02535)^{5.34} \\ A=19400\times1.143 \\ A=\text{ \ 22,174.76} \end{gathered}$

Hence, the account will be worth $22,174.76 in 32 months