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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?

Respuesta :

Part A

Using the formula for the compound interest, we have:

[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt}(A\colon\text{ future values, P: principal, r:interest,n:12,t:years)} \\ A=9000(1+\frac{0.05}{12})^{17\cdot12}\text{ (Replacing)} \\ A=\text{ }9000(1+\frac{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}[/tex]

Part B

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

[tex]\begin{gathered} A=9000(1+\frac{0.05}{4})^{17\cdot4}\text{ (Replacing)} \\ A=9000(1+\frac{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}[/tex]

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