To solve this problem, we need to apply the formula for compound interest. The formula for compound interest is:

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

Where:

• $A$ is the accumulated value (future value)
• $P$ is the principal (initial investment)
• $r$ is the annual interest rate (in decimal form)
• $n$ is the number of times the interest is compounded per year
• $t$ is the number of years

For Part 2 (b), you are asked to find the accumulated value when the interest is compounded quarterly. Here's how we apply the formula for quarterly compounding:

• $P = 15,000$
• $r = 1.45\% = 0.0145$
• $n = 4$ (since interest is compounded quarterly)
• $t = 6$ years

Now, plug in the values:

$A = 15000 \left(1 + \frac{0.0145}{4}\right)^{4 \times 6}$

Let's calculate that: Given values P = 15000 # Principal r = 0.0145 # Annual interest rate in decimal n = 4 # Compounded quarterly t = 6 # Time in years

Compound interest formula calculation

A = P * (1 + r / n)**(n * t) AThe accumulated value of the investment after 6 years, when compounded quarterly, is approximately $16,360.88.

Let me know if you need more details or have any other questions!

Here are some related questions for further exploration:

1. How would the accumulated value change if the interest rate were increased to 2%?
2. What would the accumulated value be if the interest were compounded annually?
3. How does the number of compounding periods per year affect the accumulated value?
4. What is the difference between compound interest and simple interest?
5. What is the formula for continuously compounded interest?

Tip: The more frequently the interest is compounded, the greater the accumulated value will be over time.