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.
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
Plugging in the values from the problem, we have:
A = 7000(1 + 0.033/4)^(4*25)
Simplifying the expression inside parentheses:
A = 7000(1 + 0.00825)^(100)
Calculating the values inside parentheses:
A = 7000(1.00825)^(100)
Using a calculator, we find:
A ≈ 7000(1.903142197) = $13,321.99
Rounding to the nearest cent, Anne’s final amount after 25 years of investment is $13,322.