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
