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Find the total amount to be paid back (i.e., loan + interest) on the following loans:

a. [tex]\$500[/tex] for 2 weeks at [tex]\$100[/tex] interest per week

b. [tex]\$2000[/tex] for 3 weeks at [tex]\$1[/tex] on each [tex]\$10[/tex] interest per week

c. [tex]1000[/tex] for 1 year at [tex]9\%[/tex] simple interest per annum

d. [tex]\$10000[/tex] for 15 years at [tex]8\%[/tex] simple interest per annum

e. [tex]¥60000[/tex] for 3 years at [tex]7 \frac{1}{2} \%[/tex] simple interest per annum

f. [tex]\#86000[/tex] for [tex]2 \frac{1}{2}[/tex] years at [tex]8 \frac{1}{2} \%[/tex] simple interest per annum

Answer :

Sure! Let's break down the calculations for each loan and find the total amount to be paid back, which includes both the original loan amount and the interest.

1. Loan a:
- Loan amount: [tex]$500
- Interest: $[/tex]100 per week
- Time period: 2 weeks

To calculate the total interest for 2 weeks, multiply the interest per week by the number of weeks:
[tex]\[
\text{Interest} = 100 \times 2 = 200
\][/tex]

Add the interest to the original loan amount to get the total to be paid back:
[tex]\[
\text{Total} = 500 + 200 = 700
\][/tex]

2. Loan b:
- Loan amount: [tex]$2000
- Interest: $[/tex]1 on each [tex]$10 per week
- Time period: 3 weeks

First, find the interest rate per $[/tex]10, then calculate how many [tex]$10 units are in $[/tex]2000:
[tex]\[
\frac{2000}{10} = 200
\][/tex]

Multiply the number of [tex]$10 units by the interest per unit and by the number of weeks:
\[
\text{Interest} = 200 \times 1 \times 3 = 600
\]

Add the interest to the original loan amount:
\[
\text{Total} = 2000 + 600 = 2600
\]

3. Loan c:
- Loan amount: $[/tex]1000
- Interest rate: 9% per annum
- Time period: 1 year

Calculate the simple interest using the formula:
[tex]\[
\text{Interest} = \frac{9}{100} \times 1000 \times 1 = 90
\][/tex]

Add the interest to the original loan amount:
[tex]\[
\text{Total} = 1000 + 90 = 1090
\][/tex]

4. Loan d:
- Loan amount: [tex]$10000
- Interest rate: 8% per annum
- Time period: 15 years

Calculate the simple interest:
\[
\text{Interest} = \frac{8}{100} \times 10000 \times 15 = 12000
\]

Add the interest to the original loan amount:
\[
\text{Total} = 10000 + 12000 = 22000
\]

5. Loan e:
- Loan amount: ¥60000
- Interest rate: \(7 \frac{1}{2}\%\) per annum (or 7.5%)
- Time period: 3 years

Calculate the simple interest:
\[
\text{Interest} = \frac{7.5}{100} \times 60000 \times 3 = 13500
\]

Add the interest to the original loan amount:
\[
\text{Total} = 60000 + 13500 = 73500
\]

6. Loan f:
- Loan amount: #86000
- Interest rate: \(8 \frac{1}{2}\% \) per annum (or 8.5%)
- Time period: \(2 \frac{1}{2}\) years (or 2.5 years)

Calculate the simple interest:
\[
\text{Interest} = \frac{8.5}{100} \times 86000 \times 2.5 = 18275
\]

Add the interest to the original loan amount:
\[
\text{Total} = 86000 + 18275 = 104275
\]

Therefore, the total amounts to be paid back for each loan are $[/tex]700, [tex]$2600, $[/tex]1090, $22000, ¥73500, and #104275 respectively.

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Rewritten by : Barada