Question

Dylan invested $93,000 in an account paying an interest rate of 3% compoundedquarterly. Assuming no deposits or withdrawals are made, how much money, to thenearest cent, would be in the account after 17 years?

Answer 1

The formula to calculate compound interest is given to be:

`A=P(1+(r)/(n))^(nt)`

where:

`\begin{gathered} A=\text{ final amount} \\ P=\text{ initial amount (principal)} \\ r=\text{ interest rate} \\ n=\text{ number of times interest applied per time period} \\ t=\text{ number of time period elapsed} \end{gathered}`

The following parameters are given in the question:

`\begin{gathered} P=93000 \\ r=(3)/(100)=0.03 \\ n=4(quarterly) \\ t=17\text{ years} \end{gathered}`

We can substitute these values into the formula to calculate the final amount as follows:

`A=93000(1+(0.03)/(4))^(4*17)`

Solving, we get:

`\begin{gathered} A=93000*1.0075^(68) \\ A=154,577.64 \end{gathered}`

The amount after 17 years is $154,577.64