In order to accumulate enough money for a down payment on a house, a couple deposits $ 688 per month into an account paying 6 % compounded monthly. If payments are made at the end of each period, how much money will be in the account in 4 years?
To find out how much money will be in the account in 4 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt),
where:
A is the future value of the investment,
P is the principal amount (in this case, the monthly deposits of $688),
r is the annual interest rate (6% or 0.06),
n is the number of times interest is compounded per year (monthly, so n = 12),
and t is the number of years (4).
First, let's convert the annual interest rate to a monthly interest rate: 6% / 12 = 0.005.
Next, let's calculate the future value of the investment:
A = 688(1 + 0.005/12)^(12*4)
= 688(1.0004166667)^(48)
≈ 688(1.2217295828)
≈ $840,161.37.
Therefore, after 4 years, there will be approximately $840,161.37 in the account.