Sure! Let's go through the steps to find the amount owed at the end of 1 year and 2 years for the given loan.
### Part (a): Amount Owed at the End of 1 Year
First, let's calculate the amount owed at the end of 1 year. The initial loan amount is [tex]$9000 and the interest rate is 14% per year.
Step-by-Step:
1. Convert the interest rate into a decimal form: \( 14\% = 0.14 \)
2. Use the formula for compound interest to find the amount after 1 year:
\[ \text{Amount} = \text{Principal} \times (1 + \text{Interest Rate}) \]
3. Plug in the values:
\[ \text{Amount}_{\text{year 1}} = 9000 \times (1 + 0.14) \]
4. Calculate:
\[ \text{Amount}_{\text{year 1}} = 9000 \times 1.14 = 10260 \]
So, the amount owed at the end of 1 year is $[/tex]10,260.
### Part (b): Amount Owed at the End of 2 Years
Next, we need to find the amount owed at the end of 2 years. The amount accrued at the end of 1 year is [tex]$10,260 and we will apply the same 14% interest rate for the second year.
Step-by-Step:
1. Use the amount from the end of 1 year as the principal for the second year: $[/tex]10,260.
2. Apply the same compound interest formula:
[tex]\[ \text{Amount} = \text{Principal} \times (1 + \text{Interest Rate}) \][/tex]
3. Plug in the values:
[tex]\[ \text{Amount}_{\text{year 2}} = 10260 \times (1 + 0.14) \][/tex]
4. Calculate:
[tex]\[ \text{Amount}_{\text{year 2}} = 10260 \times 1.14 = 11696.40 \][/tex]
So, the amount owed at the end of 2 years is [tex]$11,696.40.
In summary:
- The amount owed at the end of 1 year is $[/tex]10,260.
- The amount owed at the end of 2 years is $11,696.40.
