You deposit $500 each month into an account earning

Question

You deposit $500 each month into an account earning 6% interest compounded monthly. 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?

$

Answer 1

FV = PMT x [((1 + r/n)^(n*t) - 1) / (r/n)]

where FV is the future value, PMT is the periodic payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

a) To find the future value after 25 years of monthly deposits of $500 and an interest rate of 6% compounded monthly, we can plug in the values into the formula:

FV = 500 x [((1 + 0.06/12)^(12*25) - 1) / (0.06/12)] FV = 500 x [(1.06^300 - 1) / 0.005] FV = $414,456.67

Therefore, the amount in the account after 25 years will be approximately $414,456.67.

b) To find the total amount of money deposited, we can multiply the monthly deposit by the number of months in 25 years:

Total deposited = 500 x 12 x 25 Total deposited = $150,000

Therefore, the total amount of money deposited will be $150,000.

c) To find the total amount of interest earned, we can subtract the total amount deposited from the future value:

Total interest = FV - Total deposited Total interest = $414,456.67 - $150,000 Total interest = $264,456.67

Therefore, the total amount of interest earned will be $264,456.67.