Question

Benjamin invested an amount of $12,000.00 in a mutual fund. After 4 years and 6 months the accumulated value of his investment was $13,407.58. What is the nominal interest rate of the investment if interest is compounded semi-annually?__________%Round to two decimal places

Answer 1

Given:

The accumulated value of investment is A = 13,407.58.

The invested amount is P = 12,000.00.

The time period is 4 years and 6 months.

Step-by-step explanation:

The formula for the accumulated value at r rate of interest is compounded semi-annually.

`A=P(1+(r)/(200))^(2\cdot t)`

Substitute the values in the formula to determine the value of r.

`\begin{gathered} 13407.58=12000(1+(r)/(200))^(2\cdot4.5) \\ (13407.58)/(12000)=(1+(r)/(200))^9 \\ 1+(r)/(200)=((13407.58)/(12000))^{(1)/(9)} \\ (r)/(200)=1.01239-1 \\ r=0.01239\cdot200 \\ =2.478 \\ \approx2.48 \end{gathered}`

So the rate of interest is 2.48%.