To solve this problem, we can break it into two parts: the accumulation of the investment over the first 4 years, and the growth of that accumulated amount over the next 22 years without additional deposits.

Part 1: Accumulation During the First 4 Years

You invest $160 per month for 4 years into an account earning 6% interest compounded monthly.

The future value of a series of regular investments (an annuity) can be calculated using the formula:

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

Where:

• $P = 160$ (monthly payment)
• $r = \frac{0.06}{12} = 0.005$ (monthly interest rate)
• $n = 4 \times 12 = 48$ (total number of payments)

Now, let's calculate $FV_1$:

$FV_1 = 160 \times \frac{(1 + 0.005)^{48} - 1}{0.005}$

Part 2: Growth Over the Next 22 Years

After 4 years, no additional payments are made, so the amount accumulated will grow for 22 years under the same interest rate.

The future value of a lump sum investment can be calculated using:

$FV_2 = FV_1 \times (1 + r)^m$

Where:

• $FV_1$ is the future value calculated from Part 1
• $r = 0.005$ (monthly interest rate)
• $m = 22 \times 12 = 264$ (number of months)

Let's compute the final amount $FV_2$. I'll calculate this step by step.After 22 years, the final amount in the account will be approximately $32,295.36.

Would you like any further details or have any questions?

Here are five related questions you might find interesting:

1. What if the interest rate was compounded quarterly instead of monthly?
2. How would the final amount change if the monthly investment was increased to $200?
3. What if the investment period was extended to 5 years instead of 4 years?
4. How does the future value change if the interest rate was 8% instead of 6%?
5. What would the future value be if you made a one-time investment of $7,680 (equivalent to 4 years of $160 per month) instead of monthly contributions?

Tip: Regular contributions to an investment account, even if small, can significantly grow over time due to compound interest.