Question

What is the future value of $100 after 3 years if the appropriate interest rate is 8%, compounded annually? ($125.97) Compounded monthly? ($127.02

Answer 1

Answer: If compounded annually, future value =$ 125.97

If compounded monthly, future value =$ 127.18

Explanation:

Accumulated amount : $A=P(1+\dfrac{r}{n})^{nt}$, where P=principal value, t= time, n= number of periods and r =rate of interest.

Given: Principal value = $100

Time = 3 years

rate of interest : r= 0.08

If compounded annually, n=1

$A=100(1+0.08)^3=100(1.08)^3=100\times1.259712=\ 125.97$

Hence, future value =$ 125.97

If compounded monthly, n=12

$A=100(1+\dfrac{0.08}{12})^{12\times3}=100(1.0067)^{36}=100\times1.271752=\ 127.18$

Hence, future value =$ 127.18