Question

chris invests $15,000 in a retirement account with an annual compound interest rate of 3.4%
find the total amount of the investment after 27yrs
round to the nearest cent

Answer 1

To calculate the total amount of an investment with compound interest, you can use the formula:

\[
A = P (1 + r/n)^{nt}
\]

Where:
- \(A\) = the amount of money accumulated after n years, including interest.
- \(P\) = the principal amount (the initial amount of money).
- \(r\) = annual interest rate (decimal).
- \(n\) = number of times that interest is compounded per year.
- \(t\) = number of years the money is invested or borrowed.

In this case:
- \(P = 15000\)
- \(r = 0.034\) (3.4% as a decimal)
- \(n = 1\) (assuming interest is compounded once a year)
- \(t = 27\)

Now we can substitute these values into the formula:

\[
A = 15000 \times (1 + 0.034/1)^{1 \times 27}
\]

\[
A = 15000 \times (1 + 0.034)^{27}
\]

\[
A = 15000 \times (1.034)^{27}
\]

Now we calculate \( (1.034)^{27} \):

\[
(1.034)^{27} \approx 2.42436
\]

Now multiply by the principal amount:

\[
A \approx 15000 \times 2.42436 \approx 36365.40
\]

So, the total amount of the investment after 27 years is approximately **$36,365.40** when rounded to the nearest cent.