You deposit $500 each month into an account earning 3% interest compounded monthly.a) How much will you have in the account in 20 years?$b) How much total money will you put into the account?$c) How much total interest will you earn?
Question
You deposit b) How much total money will you put into the account?$c) How much total interest will you earn?
Solution
a) To calculate the future value of a series of monthly deposits, we can use the formula for the future value of a series of periodic payments (or an annuity):
FV = P * [(1 + r/n)^(nt) - 1] / (r/n)
where:
- FV is the future value of the account
- P is the monthly deposit ($500)
- r is the annual interest rate (3% or 0.03)
- n is the number of times the interest is compounded per year (12, for monthly compounding)
- t is the number of years the money is invested for (20)
Substituting the given values into the formula, we get:
FV = 500 * [(1 + 0.03/12)^(12*20) - 1] / (0.03/12)
After calculating the above expression, you will get the future value of the account after 20 years.
b) The total amount of money you put into the account is simply the amount you deposit each month times the number of months. So, over 20 years (or 240 months), you will have deposited:
Total Deposits = 120,000
c) The total interest you earn is the difference between the future value of the account (from part a) and the total amount of money you put into the account (from part b). So, once you have the future value from part a, you can calculate:
Total Interest = Future Value - Total Deposits
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