Question

Find the future value of an investment of ​$12500 if it is invested for four years and compounded semiannually at an annual rate of 4​%. Use the​ $1.00 future value table or the future value and compound interest formula.

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$12500\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 12500\left(1+(0.04)/(2)\right)^(2\cdot 4) \implies A \approx 14645.74`

Answer 2

$14,636.97

Explanation:

FV = PV x (1 + r/n)^(nt)

where r is the annual interest rate (as a decimal), n is the number of compounding periods per year, t is the number of years the money is invested, and PV is the present value.

In this case, r = 0.04 (4% as a decimal), n = 2 (since it is compounded semiannually), t = 4, and PV = $12500. Substituting these values into the formula, we get:

FV = $12500 x (1 + 0.04/2)^(2x4)

FV = $12500 x (1.02)^8

FV = $14,636.97

Therefore, the future value of the investment after four years is $14,636.97.