Question

Find the accumulated value of an investment of $10,000 for 5 years at an interest rate of 5% off the money is a. compounded quarterly and b. compounded continuously.

Answer 1

Given:

Principal amount = $10000

time = 5 years

Rate = 5%

a) compounded quarterly

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ P=10000,t=5,r=\frac{5}{100},n=4\text{ ( compounded quarterly)} \\ A=10000(1+\frac{5}{100\cdot4})^{4\cdot5} \\ A=10000(1.0125)^{20}_{} \\ A=12820.37 \end{gathered}$

The accumulated value is $12820.37.

b) Compounded continuously

$\begin{gathered} A=Pe^{rt} \\ P=10000,r=\frac{5}{100},t=5 \\ A=10000e^{\frac{5}{100}\cdot5} \\ A=10000e^{0.25} \\ A=12840.25 \end{gathered}$

The accumulated value is $12840.25.