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 total 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 or investment).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of years the money is invested or borrowed.

Plugging in the values:

- \(P = 1500\)
- \(r = 0.05\) (which is 5% written as a decimal)
- \(n = 6\)

Substituting these values into the formula gives:

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

Calculating inside the parentheses first:

\[
1 + 0.05 = 1.05
\]

Now raising it to the power of 6:

\[
(1.05)^6 \approx 1.34009564
\]

Now multiply this result by the principal:

\[
A = 1500 \times 1.34009564 \approx 2010.14346
\]

Rounding to the nearest dollar:

\[
A \approx 2010
\]

So, after 6 years, you will have approximately **$2,010** saved.