Question

An initial amount of $800 is invested in a compound savings account with an annual interest rate of 4.5%. Using the formula A = P (1 + r) Superscript t, what is the balance after five years?

$836.00
$873.62
$980.00
$996.95

Answer 1

To find the balance after five years in a compound savings account using the formula \( A = P (1 + r)^t \), we will plug in the values:

- \( P = 800 \) (the initial amount)
- \( r = 0.045 \) (the annual interest rate, expressed as a decimal)
- \( t = 5 \) (the number of years)

Substituting these values into the formula:

\[
A = 800 (1 + 0.045)^5
\]

This simplifies to:

\[
A = 800 (1.045)^5
\]

Now we need to calculate \( (1.045)^5 \):

\[
(1.045)^5 \approx 1.24659
\]

Now, multiply this result by 800:

\[
A \approx 800 \times 1.24659 \approx 996.71
\]

The balance after five years is approximately $996.71. However, this value is not one of the provided options.

However, if we were to round it:

- $996.95 is the closest option provided.

Thus, the answer is:

\[
\boxed{996.95}
\]