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 $
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (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, the principal (P) is $15,000, the annual interest rate (r) is 3.4%, or 0.034 as a decimal, interest is compounded quarterly, so n = 4, and the number of years (t) is 27.
Plugging in these values into the formula, we get:
A = 15000(1 + 0.034/4)^(4*27)
Simplifying,
A = 15000(1 + 0.0085)^(108)
Calculating,
A ≈ 15000(1.0085)^(108)
A ≈ 15000(3.509980466)
A ≈ $52,649.71
Therefore, the final amount of the investment after 27 years, compounded quarterly, is $52,649.71.
Is this right
I apologize for the mistake. Let me recalculate the answer for you.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (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, the principal (P) is $15,000, the annual interest rate (r) is 3.4%, or 0.034 as a decimal, interest is compounded quarterly, so n = 4, and the number of years (t) is 27.
Plugging in these values into the formula, we get:
A = 15000(1 + 0.034/4)^(4*27)
Simplifying,
A = 15000(1 + 0.0085)^(108)
Calculating,
A ≈ 15000(1.0085)^(108)
A ≈ 15000(2.488776595)
A ≈ $37,331.65
Therefore, the final amount of the investment after 27 years, compounded quarterly, is $37,331.65.