Question

Kaylee invested $910 in an account paying an interest rate of 2.6% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 10 years?

Answer 1

To find the amount of money in the account after 10 years with compound interest, you can use the compound interest formula:

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

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

In this case, we have:
- \( P = 910 \)
- \( r = 2.6\% = 0.026 \)
- \( n = 4 \) (since the interest is compounded quarterly)
- \( t = 10 \)

Now, plug in the values into the formula:

\[
A = 910 \left(1 + \frac{0.026}{4}\right)^{4 \times 10}
\]

First, calculate \( \frac{0.026}{4} \):

\[
\frac{0.026}{4} = 0.0065
\]

Next, calculate \( 1 + 0.0065 \):

\[
1 + 0.0065 = 1.0065
\]

Now calculate \( 4 \times 10 \):

\[
4 \times 10 = 40
\]

Now we have:

\[
A = 910 \left(1.0065\right)^{40}
\]

Next, calculate \( (1.0065)^{40} \):

\[
(1.0065)^{40} \approx 1.283682
\]

Now, multiply this result by the principal amount \( P \):

\[
A \approx 910 \times 1.283682 \approx 1166.69
\]

Rounding to the nearest dollar, the amount in the account after 10 years is:

\[
\boxed{1167}
\]