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=(5.07)/(100)=0.0507 \\ \text{Time, t(in years)=}(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+(r)/(n))^(nt)`

Thus, we have:

`\begin{gathered} A=19,400(1+(0.0507)/(2))^(2*2.67) \\ A=19400(1+0.02535)^(5.34) \\ A=19400(1.02535)^(5.34) \\ A=19400*1.143 \\ A=\text{ \$22,174.76} \end{gathered}`

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