Chris invests $15,000 in a retirement account with an annual interest rate of 3.4%. Find the final amount of the investment after 27 years if interest is compounded quarterly. Round the answer to the nearest cent.(1 point) The final amount of the investment after 27 years is $
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
Plugging in the given information:
P = $15,000
r = 0.034 (3.4% expressed as a decimal)
n = 4 (interest is compounded quarterly)
t = 27 years
A = 15,000(1 + 0.034/4)^(4*27)
A ≈ $45,693.80
The final amount of the investment after 27 years is $45,693.80.
Chris invests $15,000 in a retirement account with an annual interest rate of 3.4%. Find the final amount of the investment after 27 years if interest is compounded quarterly. Round the answer to the nearest cent.(1 point) The final amount of the investment after 27 years is $
To find the final amount of the investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
P = $15,000 (the principal investment amount)
r = 0.034 (the annual interest rate expressed as a decimal)
n = 4 (the number of times that interest is compounded per year)
t = 27 (the number of years)
Substituting these values into the formula, we get:
A = 15000(1 + 0.034/4)^(4*27)
Calculating the expression inside the parentheses:
1 + 0.034/4 = 1.0085
Calculating the expression inside the exponent:
4*27 = 108
Substituting these values back into the formula:
A = 15000(1.0085)^(108)
Calculating the value inside the parentheses:
(1.0085)^(108) ≈ 2.2435
Substituting this value back into the formula:
A = 15000 * 2.2435
Calculating the final value:
A ≈ $33,652.68
Therefore, the final amount of the investment after 27 years is $33,652.68