n order to accumulate enough money for a down payment on a house, a couple deposits $518 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 6 years?
To find out how much money will be in the account in 6 years, we need to calculate the future value of the monthly deposits compounded monthly for 6 years at an interest rate of 6%.
We can use the formula for compound interest:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = future value
PV = present value (initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
The initial deposit is $518 per month for 6 years, so PV = $518 * 12 * 6 = $37,248.
The interest rate is 6% compounded monthly, so r = 0.06/12 = 0.005.
The number of times interest is compounded per year is 12 (monthly), so n = 12.
The number of years is 6, so t = 6.
Plugging the values into the formula:
FV = 37248 * (1 + 0.005/12)^(12*6)
= 37248 * (1 + 0.0004167)^(72)
= 37248 * (1.0004167)^(72)
≈ 37248 * 1.358144
≈ $50,564
Therefore, there will be approximately $50,564 in the account in 6 years.