To solve this problem, we will use the compound interest formula:

$A = P \left( 1 + \frac{r}{n} \right)^{nt}$

where:

• $A$ is the final amount
• $P = 4500$ is the principal (initial investment)
• $r = 0.04$ (4% annual interest rate)
• $n = 4$ (since interest is compounded quarterly)
• $t = 15$ years

Step 1: Plug in the values

$A = 4500 \left( 1 + \frac{0.04}{4} \right)^{4(15)}$

$A = 4500 \left( 1 + 0.01 \right)^{60}$

$A = 4500 \times (1.01)^{60}$

Step 2: Compute $(1.01)^{60}$

Using a calculator:

$(1.01)^{60} \approx 1.8194$

Step 3: Compute final value

$A = 4500 \times 1.8194$

$A \approx 8187.30$

Final Answer:

After 15 years, the investment will be worth $8187.30.

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Would you like a breakdown of any step?

Here are some related questions to expand on this topic:

1. How does the compounding frequency affect the final investment amount?
2. What would be the value of the investment if compounded monthly instead?
3. How much total interest is earned over 15 years?
4. What is the formula for continuous compounding, and how would it change the answer?
5. What would happen if the interest rate increased to 5% per annum?

Tip: The more frequently interest is compounded, the higher the final amount due to exponential growth!