John and Rosamond want to retire in 15 years and can save $160 every three months. They plan to deposit the money at the end of each quarter into an account paying 8.72% compounded quarterly. How much will they have at the end of 15 years? (Round your answer to the nearest cent.) $
To calculate the amount John and Rosamond will have at the end of 15 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount ($160 every three months)
r = the annual interest rate (8.72% or 0.0872)
n = the number of times interest is compounded per year (quarterly, so 4)
t = the number of years the money is invested (15)
First, we need to find the quarterly interest rate:
Quarterly interest rate = 8.72% / 4 = 0.0872 / 4 = 0.0218
Now we can plug in the values and calculate the future value:
A = $160(1 + 0.0218/4)^(4*15)
A = $160(1.00545)^60
A = $160 * 2.180282
A = $348.84
Therefore, John and Rosamond will have approximately $348.84 at the end of 15 years if they save $160 every three months and deposit it into an account paying 8.72% compounded quarterly.