To calculate the accrued value of an investment with compound interest, we use the formula:

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

Where:

• $A$ is the amount of money accumulated after $t$ years, including interest.
• $P$ is the principal amount (the initial money invested).
• $r$ is the annual interest rate (decimal form).
• $n$ is the number of times the interest is compounded per year. Since the interest is compounded annually, $n = 1$.
• $t$ is the number of years.

For this question:

• $P = 10,000$
• $r = 6\% = 0.06$
• $n = 1$ (since interest is compounded annually)

Part 1: Accrued Value after 1 Year

$A = 10,000 \left( 1 + \frac{0.06}{1} \right)^{1 \times 1}$ $A = 10,000 \times (1.06)^1 = 10,600$

So, the accrued value after 1 year is $10,600.

Part 2: Accrued Value after 5 Years

$A = 10,000 \left( 1 + \frac{0.06}{1} \right)^{1 \times 5}$ $A = 10,000 \times (1.06)^5 = 10,000 \times 1.338225 = 13,382.26$

So, the accrued value after 5 years is $13,382.26.

Part 3: Accrued Value after 15 Years

$A = 10,000 \left( 1 + \frac{0.06}{1} \right)^{1 \times 15}$ $A = 10,000 \times (1.06)^{15} = 10,000 \times 2.396856 = 23,968.56$

So, the accrued value after 15 years is $23,968.56.

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Would you like me to move on to parts b and c of the problem and compute the new accrued values for interest rates of 8% and 10%?