Suppose you invest $140 a month for 6 years into an account earning 8% compounded monthly. After 6 years, you leave the money, without making additional deposits, in the account for another 30 years. How much will you have in the end?

To solve this problem, we can break it into two parts:

1. **First 6 years:** Calculate the future value of monthly investments made over 6 years with an 8% annual interest rate compounded monthly.
2. **Next 30 years:** Calculate the future value of this accumulated amount after letting it grow for another 30 years without additional contributions.

### Step 1: Calculate the Future Value of Monthly Investments for the First 6 Years

The future value of an annuity formula for monthly contributions is:
\[
FV = P \cdot \frac{(1 + i)^n - 1}{i}
\]
where:
- $ P = 140 $ (monthly contribution),
- $ i = \frac{0.08}{12} = 0.0066667 $ (monthly interest rate),
- $ n = 6 \times 12 = 72 $ (total number of contributions).

Substitute these values into the formula:

\[
FV = 140 \cdot \frac{(1 + 0.0066667)^{72} - 1}{0.0066667}
\]

Calculating this gives the future value at the end of the 6 years.

### Step 2: Let the Accumulated Amount Grow for Another 30 Years

Now, we treat the amount found in Step 1 as the principal and let it grow for another 30 years with an 8% annual interest rate compounded monthly. The compound interest formula is:

\[
A = P \cdot (1 + i)^n
\]
where:
- $ P $ is the amount found in Step 1,
- $ i = 0.0066667 $,
- $ n = 30 \times 12 = 360 $.

Substitute these values to find the final amount $ A $ after 30 years.

Let me calculate this for you.After 6 years of monthly contributions of $140, followed by 30 years of growth without additional contributions, the final amount in the account would be approximately **$140,891**.

Would you like further details on any part of this calculation?

Here are five related questions you may find useful:
1. What would happen if the interest rate changed to 6% instead of 8%?
2. How would increasing the contribution period to 10 years impact the final amount?
3. How is the future value formula for monthly contributions derived?
4. What if the contributions were made quarterly instead of monthly?
5. How does compounding frequency affect the overall future value?

**Tip:** When saving for long-term goals, increasing either the contribution period or rate of return can substantially impact the final savings due to the power of compound interest.

Learn how to calculate the final amount after investing $140 monthly for 6 years at 8% interest compounded monthly, followed by 30 years of growth without additional contributions. Includes detailed explanations of annuity and compound interest formulas. Suitable for high school students and personal finance enthusiasts.

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