To find the total amount of Kenny's investment at the end of the 5th year, we can use the future value formula for compound interest since the investment grows at 4% per year and the contributions are made at the beginning of each year.

The formula for the future value of an annuity due is:

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

• $FV$ = Future value of the investment
• $P$ = Annual investment (in this case, $12,000)
• $r$ = Interest rate per period (4% = 0.04)
• $n$ = Number of periods (5 years)

Step 1: Plug in the given values into the formula.

• $P = 12,000$
• $r = 0.04$
• $n = 5$

$FV = 12,000 \times \frac{(1 + 0.04)^5 - 1}{0.04} \times (1 + 0.04)$

Step 2: Simplify the expression inside the parentheses.

$FV = 12,000 \times \frac{(1.04)^5 - 1}{0.04} \times 1.04$

Calculate $(1.04)^5$: $(1.04)^5 \approx 1.2167$ So: $FV = 12,000 \times \frac{1.2167 - 1}{0.04} \times 1.04$ $FV = 12,000 \times \frac{0.2167}{0.04} \times 1.04$ $FV = 12,000 \times 5.4175 \times 1.04$ $FV = 12,000 \times 5.6358$ $FV \approx 67,629.57$

Final Answer:

The total amount of Kenny's investment at the end of the 5th year is $67,630 (rounded to the nearest dollar).

Would you like further details or explanations?

Here are some related questions to explore:

1. How do you calculate the future value of an investment with monthly contributions instead of annual ones?
2. What is the difference between simple interest and compound interest?
3. How would the total amount change if the interest rate was 5% instead of 4%?
4. How can you use the same formula to calculate the future value of a single lump sum investment?
5. What is the impact of increasing the number of investment years on the total future value?

Tip: Understanding the power of compounding is key when calculating future investments, as the interest earned is itself earning interest over time!