Questions: You deposit 200 each month into an account earning 8% 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?

You deposit 200 each month into an account earning 8% 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?
Transcript text: You deposit \$200 each month into an account earning 8\% interest compounded monthly. a) How much will you have in the account in 35 years? \$ $\square$ b) How much total money will you put into the account? \$ $\square$ c) How much total interest will you earn? \$ $\square$ Question Help: Video 1 Video 2 Submit Question
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Solution

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Solution Steps

Step 1: Calculate the Future Value of the Annuity

To find the total amount in the account after 35 years, we use the future value of an annuity formula: \[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \] where:

  • \( P = 200 \) (monthly deposit),
  • \( r = \frac{0.08}{12} = \frac{2}{300} \) (monthly interest rate),
  • \( n = 35 \times 12 = 420 \) (total number of deposits).

Substituting the values, we find: \[ FV = 200 \times \left( \frac{(1 + \frac{2}{300})^{420} - 1}{\frac{2}{300}} \right) \approx 458776.50 \]

Step 2: Calculate the Total Amount Deposited

The total amount deposited over 35 years is calculated as: \[ \text{Total Deposited} = P \times n = 200 \times 420 = 84000 \]

Step 3: Calculate the Total Interest Earned

The total interest earned is the difference between the future value and the total amount deposited: \[ \text{Total Interest Earned} = FV - \text{Total Deposited} = 458776.50 - 84000 \approx 374776.50 \]

Final Answer

a) \( \boxed{458776.50} \)
b) \( \boxed{84000} \)
c) \( \boxed{374776.50} \)

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