Question

You are saving money for a down payment on a motor scooter. You deposit $1,500 in a savings account that pays 5% interest compounded annually. How much will you have saved after 6 years? Round to the nearest dollar.(1 point)
$

Answer 1

To calculate the amount saved after 6 years with an initial deposit of $1,500 at an interest rate of 5% compounded annually, you can use the formula for compound interest:

\[
A = P(1 + r)^n
\]

Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial deposit).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.

Given:
- \( P = 1,500 \)
- \( r = 0.05 \)
- \( n = 6 \)

Now substitute the values into the formula:

\[
A = 1500(1 + 0.05)^6
\]

Calculating \( (1 + 0.05)^6 \):

\[
(1.05)^6 \approx 1.340095
\]

Now multiply this by the principal:

\[
A \approx 1500 \times 1.340095 \approx 2010.1425
\]

Rounding to the nearest dollar, we find:

\[
A \approx 2010
\]

So after 6 years, you will have saved approximately **$2010**.