Question

If an account is compounded annually at 9%, how much interest will a principal of $12,300 earn in 16 months? Round your answer tothe nearest cent. Note: Assume 365 days in a year and 30 days in a month.

Answer 1

From the question, we have the given information.

`\begin{gathered} \text{Principal =\$12300} \\ \text{rate}=9\text{\%} \\ \text{number of times compounded =1} \\ \text{Time =16 months =}(4)/(3)years \end{gathered}`

We will use the formula below to solve the question

`\text{Amount =P(}1+(r)/(n))^(nt)`

Therefore;

`\begin{gathered} \text{Amount}=12300(1+(9)/(100))^{(4)/(3)} \\ =12300((109)/(100))^{(4)/(3)} \\ =13797.71 \end{gathered}`

Since the Amount = 13797.71, we can get the interest by using the formula below.

`\begin{gathered} \text{Interest= Amount- Principal} \\ =13797.71-12300 \\ =1497.71 \end{gathered}`

Answer: Interest =$1497.71