Question

Jim deposited S4000 into an account with 5.9% Interest, compounded quarterly. Assuming that no withdrawals are made, how much will he have in the account

after 7 years?
Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

Write out the formula

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ \text{Where } \\ A=\text{ amount } \\ P=\text{ Principal or initial deposite} \\ r=\text{rate} \\ n=\text{ number of times compounded} \\ t=\text{ time in years } \end{gathered}`

Pick out the information given, we have

`\begin{gathered} P=4000 \\ r=(5.9)/(100)=0.059 \\ n=4 \\ t=7 \end{gathered}`

Substitute into the formula above, we have

`A=4000(1+(0.059)/(4))^(4*7)`

Simplify the expression, we obtain

`\begin{gathered} A=4000(1+0.01475)^(28) \\ A=4000(1.01475)^(28) \\ A=4000(1.5068) \\ A=6027.1732 \end{gathered}`

Therefore

After seven years there will be $6027.17 to the nearest cent

Answer: $6027.17