You deposit $300 each month into an account earning 2% interest compounded monthly

Question

a. how much will you have in the account in 15 years?

b. how much total money will you put into the account?

c. how much total interest will you earn ?

Answer 1

Question: You deposit $300 each month into an account earning 2% interest compounded monthly. Calculate: a) How much will you have in the account in 15 years? b) How much total money will you put into the account? c) How much total interest will you earn?

Answer:

a) Future Value of the Account in 15 Years: To calculate the future value of your account, we use the formula for the future value of an annuity compounded at each period: FV=P×((1+r)n−1)/rFV=P×((1+r)n−1)/r Where:

1. FV is the future value of the annuity.
2. P is the regular deposit amount ($300).
3. r is the monthly interest rate (annual rate 2% / 12).
4. n is the total number of deposits (15 years × 12 months).

After calculation, the future value of the account after 15 years is approximately $62,913.92.

b) Total Money Deposited into the Account: The total amount deposited is calculated as the monthly deposit amount multiplied by the total number of deposits. Total Deposits = $300 × (15 years × 12 months) = $54,000.

c) Total Interest Earned: The total interest earned is the difference between the future value of the account and the total amount deposited. Total Interest = Future Value - Total Deposits = $62,913.92 - $54,000 = $8,913.92.

These calculations demonstrate the benefits of regular savings and the impact of compound interest over a 15-year period.