Suppose Lisa borrows $$ \$ 7500 $$ at an interest rate of $$ 4 \% $$ compounded each year. Assume that no payments are made on the loan. Follow the instructions below. Do not do any rounding. $$ \begin{array}{l}\text { (a) Find the amount owed at the end of } 1 \text { year. } \ \text { (b) Find the amount owed at the end of } 2 \text { years. }\end{array} $$

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To find the amount owed at the end of 1 year and 2 years, we can use the formula for compound interest:

$$ A = P(1 + r)^n $$

where:
- $$ A $$ is the amount owed at the end of the loan period,
- $$ P $$ is the principal amount (initial loan amount),
- $$ r $$ is the annual interest rate (in decimal form),
- $$ n $$ is the number of years.

Given:
- Principal amount ($$ P $$) = $7500
- Annual interest rate ($$ r $$) = 4% = 0.04
- Number of years ($$ n $$) = 1 year for part (a) and 2 years for part (b)

Let's calculate the amount owed at the end of 1 year and 2 years using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$7500\left(1+0.04\right)^{1}$$
- step1: Add the numbers:
  $$7500\times 1.04^{1}$$
- step2: Calculate:
  $$7500\times 1.04$$
- step3: Multiply the numbers:
  $$7800$$
The amount owed at the end of 1 year is $7800.

Now, let's calculate the amount owed at the end of 2 years.
Calculate the value by following steps:
- step0: Calculate:
  $$7500\left(1+0.04\right)^{2}$$
- step1: Add the numbers:
  $$7500\times 1.04^{2}$$
- step2: Convert the expressions:
  $$7500\left(\frac{26}{25}\right)^{2}$$
- step3: Evaluate the power:
  $$7500\times \frac{676}{625}$$
- step4: Multiply:
  $$8112$$
The amount owed at the end of 2 years is $8112.

Therefore, the amount owed at the end of 1 year is $7800, and the amount owed at the end of 2 years is $8112.
The amount owed at the end of 1 year is $7800, and at the end of 2 years is $8112.

Suppose Lisa borrows at an interest rate of compounded each year.
Assume that no payments are made on the loan.
Follow the instructions below. Do not do any rounding.

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Suppose Lisa borrows at an interest rate of compounded each year. Assume that no payments are made on the loan. Follow the instructions below. Do not do any rounding.