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.

Answer 1

To calculate the future value of the savings with compounded interest, you can use the formula:

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

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

In this case:
- \( P = 1500 \)
- \( r = 0.05 \) (which is 5% expressed as a decimal)
- \( n = 6 \)

Now plug the values into the formula:

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

\[
A = 1500(1.05)^6
\]

Now calculate \( (1.05)^6 \):

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

Now multiply this by the principal:

\[
A \approx 1500 \times 1.340095 \approx 2010.143
\]

Rounding to the nearest dollar, you will have approximately:

\[
\boxed{2010}
\]

So after 6 years, you will have saved about $2,010 for the down payment on the motor scooter.