Use this table for problems [tex]$8-10$[/tex].
\begin{tabular}{|l|l|l|l|}
\hline Years & [tex]$11.5 \%$[/tex] & [tex]$12.5 \%$[/tex] & [tex]$13.5 \%$[/tex] \\
\hline 5 & 2.199 & 2.251 & 2.301 \\
\hline 10 & 1.406 & 1.465 & 1.523 \\
\hline 15 & 1.168 & 1.232 & 1.295 \\
\hline 20 & 0.81 & 0.87 & 0.93 \\
\hline
\end{tabular}

Find the amount of interest owed with each loan.

8. [tex]$\$[/tex]10,255[tex]$ at $[/tex]11.5 \%[tex]$ for 15 years

9. $[/tex]\[tex]$6,850$[/tex] at [tex]$12.5 \%$[/tex] for 20 years

10. [tex]$\$[/tex]2,100[tex]$ at $[/tex]13.5 \%$ for 5 years



Answer :

Let's solve each problem step by step.

### Problem 8: [tex]$10,255$[/tex] at [tex]$11.5\%$[/tex] for 15 years

1. Loan Details:
- Principal amount: [tex]$10,255 - APR: $[/tex]11.5\%[tex]$ - Period: 15 years - Monthly payment per $[/tex]100: [tex]$1.168$[/tex]

2. Calculate the Monthly Payment:
- Monthly payment = [tex]\(\frac{10,255}{100} \times 1.168\)[/tex]

[tex]\[ \text{Monthly payment} = 102.55 \times 1.168 = 119.7984 \][/tex]

3. Calculate the Total Payment Over the Loan Period:
- Total months: [tex]\(15 \times 12 = 180\)[/tex]
- Total payment = [tex]\(119.7984 \times 180\)[/tex]

[tex]\[ \text{Total payment} = 119.7984 \times 180 = 21,563.712 \][/tex]

4. Calculate the Total Interest Owed:
- Interest owed = Total payment - Principal amount

[tex]\[ \text{Interest owed} = 21,563.712 - 10,255 = 11,308.712 \][/tex]

### Problem 9: [tex]$6,850$[/tex] at [tex]$12.5\%$[/tex] for 20 years

1. Loan Details:
- Principal amount: [tex]$6,850 - APR: $[/tex]12.5\%[tex]$ - Period: 20 years - Monthly payment per $[/tex]100: [tex]$0.87$[/tex]

2. Calculate the Monthly Payment:
- Monthly payment = [tex]\(\frac{6,850}{100} \times 0.87\)[/tex]

[tex]\[ \text{Monthly payment} = 68.5 \times 0.87 = 59.595 \][/tex]

3. Calculate the Total Payment Over the Loan Period:
- Total months: [tex]\(20 \times 12 = 240\)[/tex]
- Total payment = [tex]\(59.595 \times 240\)[/tex]

[tex]\[ \text{Total payment} = 59.595 \times 240 = 14,303.304 \][/tex]

4. Calculate the Total Interest Owed:
- Interest owed = Total payment - Principal amount

[tex]\[ \text{Interest owed} = 14,303.304 - 6,850 = 7,453.304 \][/tex]

### Problem 10: [tex]$2,100$[/tex] at [tex]$13.5\%$[/tex] for 5 years

1. Loan Details:
- Principal amount: [tex]$2,100 - APR: $[/tex]13.5\%[tex]$ - Period: 5 years - Monthly payment per $[/tex]100: [tex]$2.301$[/tex]

2. Calculate the Monthly Payment:
- Monthly payment = [tex]\(\frac{2,100}{100} \times 2.301\)[/tex]

[tex]\[ \text{Monthly payment} = 21 \times 2.301 = 48.321 \][/tex]

3. Calculate the Total Payment Over the Loan Period:
- Total months: [tex]\(5 \times 12 = 60\)[/tex]
- Total payment = [tex]\(48.321 \times 60\)[/tex]

[tex]\[ \text{Total payment} = 48.321 \times 60 = 2,899.26 \][/tex]

4. Calculate the Total Interest Owed:
- Interest owed = Total payment - Principal amount

[tex]\[ \text{Interest owed} = 2,899.26 - 2,100 = 799.26 \][/tex]

### Summary:

1. Amount of interest owed for [tex]$10,255 at $[/tex]11.5\%[tex]$ for 15 years: $[/tex]11305.112
2. Amount of interest owed for [tex]$6,850 at $[/tex]12.5\%[tex]$ for 20 years: $[/tex]7452.800
3. Amount of interest owed for [tex]$2,100 at $[/tex]13.5\%[tex]$ for 5 years: $[/tex]799.26