Question

1. You invest $28,000 into an account earning 9.3% interest compounded monthly. This interest is used for both parts.A. How much money is in the account after 5 years? Be sure to show the formula you used with the numbers plugged in to find the solution.B. How much money is in the account after 29 years? Be sure to show the equation you used with the numbers plugged in to find the solution.

Answer 1

A.

In order to calculate the amount after 5 years for compound interest, we can use the formula:

`P=P_0\cdot(1+(i)/(n))^(nt)`

Where P is the final amount after t years, P0 is the initial value, i is the interest rate and n depends on the compound period (since it's monthly, let's use n = 12).

So we have:

`\begin{gathered} P=28000(1+(0.093)/(12))^(5\cdot12) \\ P=28000\cdot(1+0.00775)^(60) \\ P=44496.56 \end{gathered}`

B.

For t = 29, we have:

`\begin{gathered} P=28000\cdot(1.00775)^(12\cdot29) \\ P=411088.01 \end{gathered}`