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.
The final amount of the investment after 27 years is $___
To find the final amount of the investment after 27 years with quarterly compounding, we use the formula:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal amount ($15,000)
r = the annual interest rate (3.4% or 0.034 as a decimal)
n = the number of times interest is compounded per year (quarterly, so n = 4)
t = the number of years (27)
Plugging in the values:
A = 15000(1 + 0.034/4)^(4*27)
Calculating inside parentheses:
A = 15000(1.0085)^(108)
Calculating the exponent:
A = 15000(3.2445)
Multiplying:
A = 48667.50
Rounding to the nearest cent:
A ≈ $48,667.50
Therefore, the final amount of the investment after 27 years is $48,667.50.
are you sure?
Apologies for the mistake. Let's recalculate the final amount:
A = 15000(1 + (0.034/4))^(4*27)
Calculating inside parentheses:
A = 15000(1.0085)^(108)
Calculating the exponent:
A ≈ 15000(1.3498588074)
Multiplying:
A ≈ 20,247.88
Rounding to the nearest cent:
A ≈ $20,247.88
Therefore, the final amount of the investment after 27 years is $20,247.88.