Suppose you invest $140 a month for 3 years into an account earning 8% compounded monthly. After 3 years, you leave the money, without making additional deposits, in the account for another 26 years. How much will you have in the end?

To solve this problem, we will break it into two phases:

### Phase 1: Monthly Contributions for 3 Years
You are investing $140 per month for 3 years into an account earning 8% interest compounded monthly. We use the **future value of a series** formula for this phase:

\[
FV_1 = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $ P = 140 $ (monthly deposit),
- $ r = \frac{8\%}{12} = \frac{0.08}{12} = 0.0066667 $ (monthly interest rate),
- $ n = 3 \times 12 = 36 $ (total number of deposits over 3 years).

### Phase 2: Letting the Amount Grow for 26 Years Without Additional Contributions
After 3 years, the accumulated money will stay in the account for another 26 years, earning the same 8% interest compounded monthly. For this, we use the **future value of a lump sum** formula:

\[
FV_2 = FV_1 \times (1 + r)^n
\]

Where:
- $ r = 0.0066667 $ (monthly interest rate),
- $ n = 26 \times 12 = 312 $ (number of months over 26 years).

Now, let's calculate the final amount.The total amount you will have at the end of 29 years, after contributing $140 per month for the first 3 years and letting the accumulated amount grow for 26 more years, will be approximately **$45,112.71**.

Would you like any further details or clarifications?

Here are 5 related questions to consider:
1. How would the final amount change if the interest rate was higher?
2. What happens if you make deposits for more than 3 years?
3. How would the total change with a different compounding period (e.g., quarterly)?
4. How does the final amount differ if the initial deposit was larger?
5. How much would you have if you kept contributing during the 26 years?

**Tip**: The longer the compounding period (i.e., the more frequently interest is compounded), the higher the total amount due to the compounding effect!

Learn how to calculate the future value of a monthly investment of $140 over 3 years with an 8% interest rate compounded monthly, followed by 26 years of growth without additional deposits. Includes detailed steps and formulas for compound interest calculations.

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