Anne invests $7,000 into a retirement account with a compound interest rate of 3.3% compounded quarterly. What is Anne's final amount after 25 years of investment? Round the answer to the nearest cent. (1 point)
Anne's final amount after 25 years of investment can be calculated using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount after t time
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Using the given information:
P = $7,000
r = 3.3% = 0.033 (expressed as a decimal)
n = 4 (quarterly compounding)
t = 25
Plugging in the values, we have:
A = 7000(1 + 0.033/4)^(4*25)
A = 7000(1 + 0.00825)^(100)
A ≈ 7000(1.00825)^100
A ≈ 7000(1.960993831)
A ≈ $13,726.96
Therefore, Anne's final amount after 25 years of investment is approximately $13,726.96.