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
To calculate the final amount after 25 years of investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the initial investment
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Plugging in the given values:
P = $7,000
r = 3.3% = 0.033 (as a decimal)
n = 4 (compounded quarterly)
t = 25 years
A = $7,000(1 + 0.033/4)^(4*25)
A = $7,000(1.00825)^(100)
Using a calculator, we find that (1.00825)^(100) ≈ 1.36864
A ≈ $7,000 * 1.36864
A ≈ $9570.47
Therefore, Anne's final amount after 25 years of investment is approximately $9,570.47.
wrong
Apologies for the mistake. Let's recalculate correctly.
P = $7,000
r = 3.3% = 0.033 (as a decimal)
n = 4 (compounded quarterly)
t = 25 years
A = P(1 + r/n)^(nt)
A = 7000(1 + 0.033/4)^(4*25)
A ≈ 7000(1 + 0.00825)^(100)
Using a calculator, we find that (1.00825)^(100) ≈ 2.2032
A ≈ 7000 * 2.2032
A ≈ 15422.40
Therefore, Anne's final amount after 25 years of investment is approximately $15,422.40