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. What is the answer?
The formula to calculate the final amount with compound interest is:
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 that interest is compounded per year
t = number of years
In this case, Anne invests $7,000 at an annual interest rate of 3.3%, compounded quarterly, for 25 years. Plugging in the values into the formula:
A = 7000*(1 + 0.033/4)^(4*25)
Simplifying the equation:
A = 7000*(1 + 0.00825)^100
Calculating the inside of the parentheses:
1 + 0.00825 ≈ 1.00825
A = 7000*(1.00825)^100
Calculating the exponent:
(1.00825)^100 ≈ 1.348
A ≈ 7000*1.348
A ≈ 9416
Rounding to the nearest cent:
A ≈ $9416.00
Anne's final amount after 25 years of investment is approximately $9416.00.