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.
Anne's final amount after 25 years of investment is $____.
To find the final amount after 25 years of investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, Anne's principal amount is $7,000, the annual interest rate is 3.3% (0.033 as a decimal), interest is compounded quarterly (n = 4), and she invests for 25 years (t = 25).
A = 7000(1 + 0.033/4)^(4 * 25)
Calculating this using a calculator (or a spreadsheet software):
A ≈ $15,802.88
Therefore, Anne's final amount after 25 years of investment is approximately $15,802.88.