You deposit $500 each month into an account earning 7% interest compounded monthly.
Round your answers to the nearest whole dollar.
a) How much will you have in the account in 25 years?
$
b) How much total money will you put into the account?
$
c) How much total interest will you earn?
$
To calculate the amount in the account in 25 years, we will use the formula for compound interest:
A = P (1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal investment/loan amount
r = annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
a) For this question, P = $500, r = 7% = 0.07 (as a decimal), n = 12 (compounded monthly), and t = 25 years.
A = 500 (1 + 0.07/12)^(12*25)
A ≈ $2,038.76
So, you will have approximately $2,038 in the account in 25 years.
b) To calculate the total money you put into the account, we need to multiply the monthly deposit by the number of months:
Total money put into the account = Monthly deposit x Number of months
Total money put into the account = $500 x 12 x 25
Total money put into the account = $150,000
So, you will put a total of $150,000 into the account.
c) To calculate the total interest earned, we subtract the total amount of money you put into the account from the final amount in the account:
Total interest earned = Final amount - Total money put into the account
Total interest earned = $2,038 - $150,000
Total interest earned ≈ -$147,962
Notice that the total interest earned is negative. This is because the total amount put into the account is greater than the final amount due to the effect of compounding. So, you will earn approximately -$147,962 in interest.