To find the future value of Mary's investment using the compound interest formula, we follow these steps:
1. Identify the given values:
- Principal amount ([tex]\( P \)[/tex]) = \[tex]$1000
- Annual interest rate (\( r \)) = 0.05 (since 5% as a decimal is 0.05)
- Number of times interest is compounded per year (\( n \)) = 4
- Number of years (\( t \)) = 5
2. Write the compound interest formula:
\[
R = P \left(1 + \frac{r}{n}\right)^{nt}
\]
3. Substitute the given values into the formula:
\[
R = 1000 \left(1 + \frac{0.05}{4}\right)^{4 \cdot 5}
\]
4. Calculate the value inside the parentheses:
\[
1 + \frac{0.05}{4} = 1 + 0.0125 = 1.0125
\]
5. Calculate the exponent:
\[
nt = 4 \cdot 5 = 20
\]
6. Raise the value inside the parentheses to the power of 20:
\[
(1.0125)^{20}
\]
7. Multiply this result by the principal amount (\( P \)):
\[
R = 1000 \times (1.0125)^{20} \approx 1000 \times 1.2820372317085844
\]
8. Calculate the final amount:
\[
R \approx 1282.0372317085844
\]
So, the future value of Mary's investment after 5 years will be approximately \$[/tex]1,282.04.
Based on the calculations, the correct answer is:
[tex]\[
\$ 1,282.04
\][/tex]
