Questions: You deposit 360 each month into an account earning 3.2% interest compounded monthly. a) How much will you have in the account in 35 years? b) How much total money will you put into the account? c) How much total interest will you earn?

Solution Steps

To solve this problem, we need to use the formula for the future value of a series of regular deposits (an annuity). The future value of an annuity formula is:

\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]

where:

• \( P \) is the monthly deposit amount.
• \( r \) is the monthly interest rate (annual rate divided by 12).
• \( n \) is the total number of deposits (months).

a) Calculate the future value using the formula above. b) Calculate the total money deposited by multiplying the monthly deposit by the number of months. c) Subtract the total deposits from the future value to find the total interest earned.

To find the future value of the annuity, we use the formula:

\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]

where:

• \( P = 360 \)
• \( r = \frac{0.032}{12} = 0.002667 \)
• \( n = 35 \times 12 = 420 \)

Substituting these values, we get:

\[ FV = 360 \times \frac{(1 + 0.002667)^{420} - 1}{0.002667} \approx 278139 \]

The total money deposited over 35 years is:

\[ \text{Total Deposited} = 360 \times 420 = 151200 \]

The total interest earned is the future value minus the total deposited:

\[ \text{Total Interest} = 278139 - 151200 = 126939 \]

Final Answer