Solve.
B) DeShawn invests $1,179 in a retirement
account with a fixed annual interest rate of
8% compounded 12 times per year. What
will the account balance be after 15 years?



Answer :

To solve the problem of finding the future value of an investment with compound interest, we can use the compound interest formula:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

where:
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( r \)[/tex] is the annual interest rate (in decimal form),
- [tex]\( n \)[/tex] is the number of times the interest is compounded per year,
- [tex]\( t \)[/tex] is the number of years the money is invested,
- [tex]\( A \)[/tex] is the amount of money accumulated after [tex]\( t \)[/tex] years, including interest.

Let's identify the given values:
- Principal amount ([tex]\( P \)[/tex]) = [tex]$1,179 - Annual interest rate (\( r \)) = 8% = 0.08 (in decimal form) - Number of times interest is compounded per year (\( n \)) = 12 - Number of years (\( t \)) = 15 Substituting these values into the formula, we have: \[ A = 1179 \left(1 + \frac{0.08}{12}\right)^{12 \cdot 15} \] Calculate the value inside the parentheses first: \[ \left(1 + \frac{0.08}{12}\right) \] \[ 1 + \frac{0.08}{12} = 1 + 0.00666667 \approx 1.00666667 \] Now, raise this value to the power of \( 12 \cdot 15 \): \[ \left(1.00666667\right)^{180} \] Use a calculator to find the value of \( 1.00666667^{180} \): \[ 1.00666667^{180} \approx 3.308286 \] Finally, multiply this value by the principal amount: \[ A = 1179 \times 3.308286 \approx 3,900.26 \] So, the account balance after 15 years will be approximately $[/tex]3,900.26.