Question

At the time of her grandson's birth, a grandmother deposited $9,000 in an account. The account was paying 5.0% interest compounded monthly.a. If the rate did not change, what was the value of the account after 17 years?b. If the money had been invested at 5.0% compounded quarterly, what would the value of the account have been after 17 years?

Answer 1

Part A

Using the formula for the compound interest, we have:

`\begin{gathered} A=P(1+(r)/(n))^(nt)(A\colon\text{ future values, P: principal, r:interest,n:12,t:years)} \\ A=9000(1+(0.05)/(12))^(17\cdot12)\text{ (Replacing)} \\ A=\text{ }9000(1+(0.05)/(12))^(204)(\text{ Multiplying)} \\ A=\text{ }9000(1+0.0042)^(204)(\text{Dividing)} \\ A=\text{ }9000(1.0042)^(204)(\text{ Adding)} \\ A=21019.67\text{ (Raising 1.0042 to the power of 204 and multiplying)} \\ \text{ The future value is \$21019.67} \end{gathered}`

Part B

Using the formula for the compound interest 5% quarterly, we have:

`\begin{gathered} A=9000(1+(0.05)/(4))^(17\cdot4)\text{ (Replacing)} \\ A=9000(1+(0.05)/(4))^(68)\text{ (Multiplying)} \\ A=9000(1+0.0125)^(68)\text{ (Dividing)} \\ A=9000(1.0125)^(68)(\text{ Adding)} \\ A=20946.17\text{ (Raising 1.0125 to the power of 68 and multiplying)} \\ \text{The answer is \$20946.17} \end{gathered}`