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+(r)/(n))^(nt) \\ P=10000,t=5,r=(5)/(100),n=4\text{ ( compounded quarterly)} \\ A=10000(1+(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=(5)/(100),t=5 \\ A=10000e^{(5)/(100)\cdot5} \\ A=10000e^(0.25) \\ A=12840.25 \end{gathered}`

The accumulated value is $12840.25.