Question

Suppose you deposit $2,417.00 into an account today. In 8.00 years the account is worth $3,792.00. The account earned ____% per year.

Answer 1

To find the annual interest rate, we can use the formula for compound interest, which relates the present value (PV), future value (FV), interest rate (r), and time (t):

\[
FV = PV \times (1 + r)^t
\]

In this case:

- \(FV = 3,792.00\)
- \(PV = 2,417.00\)
- \(t = 8.00\)

We need to solve for \(r\). Rearranging the equation gives us:

\[
(1 + r)^t = \frac{FV}{PV}
\]

Substituting the known values:

\[
(1 + r)^8 = \frac{3,792.00}{2,417.00}
\]

Calculating the right side:

\[
\frac{3,792.00}{2,417.00} \approx 1.5706
\]

Now, we need to take the eighth root of both sides to solve for \(1 + r\):

\[
1 + r = (1.5706)^{\frac{1}{8}}
\]

Calculating the eighth root:

\[
1 + r \approx 1.0614
\]

Now, subtract 1 to find \(r\):

\[
r \approx 1.0614 - 1 = 0.0614
\]

To convert \(r\) to a percentage:

\[
r \approx 0.0614 \times 100 \approx 6.14\%
\]

Thus, the account earned approximately **6.14%** per year.