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.

1 answer

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.