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 after 27 years with quarterly compounding, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of the investment
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
Plugging in the given values:
P = $15,000
r = 3.4% = 0.034
n = 4 (compounded quarterly)
t = 27
A = 15000(1 + 0.034/4)^(4*27)
Calculating this equation will give us the final amount of the investment after 27 years.
So what’s the answer
Calculating the equation:
A = 15000(1 + 0.034/4)^(4*27)
A ≈ $40,767.46
Therefore, the final amount of the investment after 27 years, rounded to the nearest cent, is approximately $40,767.46.
When Martin was born, his father
set up a $5,000 college fund for him
with an annual compound interest
rate of 7.3%. What is the final
amount of this college fund, and
how much interest is gained if this
fund is invested for 18 years if
interest is compounded monthly?
Round the answers to two decimal
places as needed. (1 point)
The final amount of the college
fund is $, and the amount of
interest gained is $
To find the final amount of the college fund after 18 years with monthly compounding, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of the college fund
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
Plugging in the given values:
P = $5,000
r = 7.3% = 0.073
n = 12 (compounded monthly)
t = 18
A = 5000(1 + 0.073/12)^(12*18)
Calculating this equation will give us the final amount of the college fund after 18 years.