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Question

John decides to start saving money for a new car. He knows he can invest money into an account which will earn a 6.5% APR, compounded weekly, and would like to have saved $10,000 after 5 years. a. How much money will he need to invest into the account now so that he has$10,000 after 5 years? b. Determine the APY (Annual Percent Yield) for the account. c. Determine the 5-year percent change for the account.

Solution

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Answered 2 years ago
Answered 2 years ago
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AA

There is the formula:

A=p(1+rn)nt\begin{aligned} A&=p\left(1+\dfrac{r}{n}\right)^{nt}\\ \end{aligned}

He wants to save $10000\$10000, so A=10000A=10000 After 55 years means t=5t=5 6,5%6,5\% APR compounded weekly means r=0,065r=0,065 and n=3657=52n=\dfrac{365}{7}=52

Let us find AA:

A=p(1+rn)nt10000=p(1+0,06552)525p=10000(1+0,06552)525p=7226,74\begin{aligned} A&=p\left(1+\dfrac{r}{n}\right)^{nt}\\ \\ 10000&=p\left(1+\dfrac{0,065}{52}\right)^{52\cdot5}\\ \\ p&=\dfrac{10000}{\left(1+\dfrac{0,065}{52}\right)^{52\cdot5}}\\ \\ &\boxed{p=7226,74} \end{aligned}

Thus, he will need to invest $7226,74\$7226,74 into the account now so that he has $10000\$10000 after 55 years.

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