Answer:
A = $35,198.32
Step-by-step explanation:
Use the formula to calculate compound interest:
A = P(1 + i)ⁿ
"A" for total amount after the time period
"P" for principal, or starting money
"i" for the interest rate in a compounding period
To calculate "i":
i = r / c
"n" for the number of compounding periods
To calculate "n":
n = tc
So, we can combine the formulas into:
[tex]A = P(1+\frac{r}{c})^{tc}[/tex]
"c" is the compounding periods in a year. (quarterly = 4)
We know:
P = 8000
r = 10% / 100 = 0.1
t = 15
c = 4
Substitute the information in the formula.
[tex]A = P(1+\frac{r}{c})^{tc}[/tex]
[tex]A = 8000(1+\frac{0.1}{4})^{15*4}[/tex] Solve "i" and "n"
[tex]A = 8000(1+0.025)^{60}[/tex] Solve inside the brackets
[tex]A = 8000(1.025)^{60}[/tex] Do the exponent before multiplying by 8000
A = 35198.318 Exact answer
A ≈ 35198.32 Round to two decimal places for money
Therefore she will have $35,198.32 after 15 years.
