Answer :
Let's solve each part of this exercise by calculating the total amount to be paid back for each loan, which combines both the principal and the interest.
1. Loan a: ¥500 for 2 weeks at ¥100 interest per week.
- Principal amount ([tex]\(P\)[/tex]): ¥500
- Interest per week: ¥100
- Duration: 2 weeks
Calculation:
- Total interest = Interest per week × Number of weeks = ¥100 × 2 = ¥200
- Total amount to be paid back = Principal + Total interest = ¥500 + ¥200 = ¥700
2. Loan b: ¥2000 for 3 weeks at ¥1 per ¥10 interest per week.
- Principal amount ([tex]\(P\)[/tex]): ¥2000
- Interest rate: ¥1 for every ¥10 per week
- Duration: 3 weeks
Calculation:
- Interest per week = (Principal / 10) × Interest rate = (¥2000 / 10) × ¥1 = ¥200
- Total interest = Interest per week × Number of weeks = ¥200 × 3 = ¥600
- Total amount to be paid back = Principal + Total interest = ¥2000 + ¥600 = ¥2600
3. Loan c: ¥1000 for 1 year at 9% simple interest per annum.
- Principal amount ([tex]\(P\)[/tex]): ¥1000
- Interest rate (annual): 9%
- Duration: 1 year
Calculation:
- Annual interest = Principal × Interest rate × Time = ¥1000 × 0.09 × 1 = ¥90
- Total amount to be paid back = Principal + Interest = ¥1000 + ¥90 = ¥1090
4. Loan d: ¥10000 for 15 years at 8% simple interest per annum.
- Principal amount ([tex]\(P\)[/tex]): ¥10000
- Interest rate (annual): 8%
- Duration: 15 years
Calculation:
- Total interest = Principal × Interest rate × Time = ¥10000 × 0.08 × 15 = ¥12000
- Total amount to be paid back = Principal + Total interest = ¥10000 + ¥12000 = ¥22000
5. Loan e: ¥60000 for 3 years at [tex]\(7 \frac{1}{2}\)[/tex]% simple interest per annum.
- Principal amount ([tex]\(P\)[/tex]): ¥60000
- Interest rate (annual): [tex]\(7.5\)[/tex]%
- Duration: 3 years
Calculation:
- Total interest = Principal × Interest rate × Time = ¥60000 × 0.075 × 3 = ¥13500
- Total amount to be paid back = Principal + Total interest = ¥60000 + ¥13500 = ¥73500
6. Loan f: ¥86000 for [tex]\(2 \frac{1}{2}\)[/tex] years at [tex]\(8 \frac{1}{2}\)[/tex]% simple interest per annum.
- Principal amount ([tex]\(P\)[/tex]): ¥86000
- Interest rate (annual): [tex]\(8.5\)[/tex]%
- Duration: [tex]\(2.5\)[/tex] years
Calculation:
- Total interest = Principal × Interest rate × Time = ¥86000 × 0.085 × 2.5 = ¥18275
- Total amount to be paid back = Principal + Total interest = ¥86000 + ¥18275 = ¥104275
Each calculation shows how to find the total amount to be paid back on a loan by adding the principal to the total interest accrued over the given time period.
1. Loan a: ¥500 for 2 weeks at ¥100 interest per week.
- Principal amount ([tex]\(P\)[/tex]): ¥500
- Interest per week: ¥100
- Duration: 2 weeks
Calculation:
- Total interest = Interest per week × Number of weeks = ¥100 × 2 = ¥200
- Total amount to be paid back = Principal + Total interest = ¥500 + ¥200 = ¥700
2. Loan b: ¥2000 for 3 weeks at ¥1 per ¥10 interest per week.
- Principal amount ([tex]\(P\)[/tex]): ¥2000
- Interest rate: ¥1 for every ¥10 per week
- Duration: 3 weeks
Calculation:
- Interest per week = (Principal / 10) × Interest rate = (¥2000 / 10) × ¥1 = ¥200
- Total interest = Interest per week × Number of weeks = ¥200 × 3 = ¥600
- Total amount to be paid back = Principal + Total interest = ¥2000 + ¥600 = ¥2600
3. Loan c: ¥1000 for 1 year at 9% simple interest per annum.
- Principal amount ([tex]\(P\)[/tex]): ¥1000
- Interest rate (annual): 9%
- Duration: 1 year
Calculation:
- Annual interest = Principal × Interest rate × Time = ¥1000 × 0.09 × 1 = ¥90
- Total amount to be paid back = Principal + Interest = ¥1000 + ¥90 = ¥1090
4. Loan d: ¥10000 for 15 years at 8% simple interest per annum.
- Principal amount ([tex]\(P\)[/tex]): ¥10000
- Interest rate (annual): 8%
- Duration: 15 years
Calculation:
- Total interest = Principal × Interest rate × Time = ¥10000 × 0.08 × 15 = ¥12000
- Total amount to be paid back = Principal + Total interest = ¥10000 + ¥12000 = ¥22000
5. Loan e: ¥60000 for 3 years at [tex]\(7 \frac{1}{2}\)[/tex]% simple interest per annum.
- Principal amount ([tex]\(P\)[/tex]): ¥60000
- Interest rate (annual): [tex]\(7.5\)[/tex]%
- Duration: 3 years
Calculation:
- Total interest = Principal × Interest rate × Time = ¥60000 × 0.075 × 3 = ¥13500
- Total amount to be paid back = Principal + Total interest = ¥60000 + ¥13500 = ¥73500
6. Loan f: ¥86000 for [tex]\(2 \frac{1}{2}\)[/tex] years at [tex]\(8 \frac{1}{2}\)[/tex]% simple interest per annum.
- Principal amount ([tex]\(P\)[/tex]): ¥86000
- Interest rate (annual): [tex]\(8.5\)[/tex]%
- Duration: [tex]\(2.5\)[/tex] years
Calculation:
- Total interest = Principal × Interest rate × Time = ¥86000 × 0.085 × 2.5 = ¥18275
- Total amount to be paid back = Principal + Total interest = ¥86000 + ¥18275 = ¥104275
Each calculation shows how to find the total amount to be paid back on a loan by adding the principal to the total interest accrued over the given time period.
