In order to accumulate enough money for a down payment on a house, a couple deposits $758 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 7 years?

Question

Genesis Allen · Accepted Answer

About $79,000, but I wonder if this question is in the right category.

#A=R*[(1+r/n)^(nt)-1]/(r/n)# is the annuity formula, which is what you'd use for regular payments being made over the course of time r=0.06 (r is the interest rate as decimal) R=$758 (R stands for the monthly payment) n=12 because 12 payments per year t = 7 for 7 years #A=758*[(1+.06/12)^(12*7)-1]/(.06/12)# #A=758[(.5204]/(.005)]=$78,892.54#

Eli Assouline · Answer

undefined To calculate the future value of the investment, you can use the formula for compound interest:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

Where:
FV = future value
P = initial deposit or payment (monthly deposit in this case)
r = annual interest rate (in decimal form, so 6% becomes 0.06)
n = number of times interest is compounded per year (monthly compounding in this case)
t = time in years

Plugging in the given values:
P = $758
r = 0.06
n = 12 (monthly compounding)
t = 7

FV = 758 * ((1 + 0.06/12)^(12*7) - 1) / (0.06/12)

FV ≈ $69,086.68

So, there will be approximately $69,086.68 in the account after 7 years.