Suppose Henry borrows $3500 at an interest rate of 13% compounded each year. Assume the No payments are made on the loan. Follow the instructions below. Do not do any rounding. (A) find the amount owed at the end of year 1. (B) find the Amount owed at the end of 2 years.

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

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

Where:
- $A$ is the amount owed after $t$ years.
- $P$ is the principal amount (initial amount borrowed).
- $r$ is the annual interest rate (as a decimal).
- $n$ is the number of times the interest is compounded per year.
- $t$ is the number of years.

In this case:
- $P = 3500$ dollars
- $r = 0.13$ (since 13% is equivalent to 0.13 as a decimal)
- $n = 1$ (since the interest is compounded annually)
- $t = 1$ for part (A) and $t = 2$ for part (B).

### Part (A) - Amount Owed at the End of Year 1

For $t = 1$:

\[
A_1 = 3500 \left(1 + \frac{0.13}{1}\right)^{1 \times 1}
\]

Simplifying:

\[
A_1 = 3500 \left(1 + 0.13\right)^{1}
\]

\[
A_1 = 3500 \times 1.13
\]

\[
A_1 = 3955
\]

So, the amount owed at the end of year 1 is **$3955**.

### Part (B) - Amount Owed at the End of 2 Years

For $t = 2$:

\[
A_2 = 3500 \left(1 + \frac{0.13}{1}\right)^{1 \times 2}
\]

Simplifying:

\[
A_2 = 3500 \times 1.13^2
\]

\[
A_2 = 3500 \times 1.2769
\]

\[
A_2 = 4469.15
\]

So, the amount owed at the end of 2 years is **$4469.15**.

### Summary:
- **(A)** The amount owed at the end of year 1 is **$3955**.
- **(B)** The amount owed at the end of year 2 is **$4469.15**.

Would you like more details or have any questions?  

Here are some related questions:
1. How would the amount change if the interest were compounded quarterly?
2. What if the interest rate were 10% instead of 13%?
3. How would the total interest be calculated after 2 years?
4. What is the formula to find the amount owed after 3 years?
5. How does changing the compounding frequency affect the amount owed?
6. Can you calculate the amount owed after 5 years with the same conditions?
7. What is the effective annual rate (EAR) for this loan?
8. How would the amount differ if payments were made annually?

**Tip:** When dealing with compounded interest, always remember to adjust the interest rate and the time period according to the compounding frequency.

Learn how to calculate compound interest on a $3500 loan borrowed at 13% interest annually. Find out the amount owed after 1 and 2 years with detailed step-by-step solutions. Suitable for high school students studying financial mathematics.

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