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**Problem 3:**
- **Monthly Instalment:** R252.05
**Problem 4:**
- **Total Amount to Pay:** R96,162.50
Solución
Let's solve each problem step by step.
### Problem 3: Mr. Hassiem's Computer Hire Purchase
**Known Conditions:**
- Price of the computer: \( P = 8999 \)
- Deposit paid: \( D = 1500 \)
- Simple interest rate: \( r = 7\% \) per annum
- Time period: \( t = 3 \) years
**Step 1: Calculate the amount financed.**
The amount financed is the price of the computer minus the deposit:
\[
A = P - D = 8999 - 1500 = 7499
\]
**Step 2: Calculate the total interest over 3 years.**
Using the formula for simple interest:
\[
I = A \cdot r \cdot t
\]
where \( r \) is in decimal form:
\[
r = \frac{7}{100} = 0.07
\]
Now, substituting the values:
\[
I = 7499 \cdot 0.07 \cdot 3
\]
**Step 3: Calculate the total amount to be paid back.**
The total amount to be paid back is the amount financed plus the interest:
\[
T = A + I
\]
**Step 4: Calculate the monthly instalment.**
The total number of months over 3 years is:
\[
n = 3 \cdot 12 = 36
\]
The monthly instalment \( M \) is given by:
\[
M = \frac{T}{n}
\]
Now, let's perform the calculations.
### Problem 4: Abusiswe's Car Loan
**Known Conditions:**
- Loan amount: \( L = 78500 \)
- Simple interest rate: \( r = 7.5\% \) per annum
- Time period: \( t = 3 \) years
**Step 1: Calculate the total interest over 3 years.**
Using the formula for simple interest:
\[
I = L \cdot r \cdot t
\]
where \( r \) is in decimal form:
\[
r = \frac{7.5}{100} = 0.075
\]
Now, substituting the values:
\[
I = 78500 \cdot 0.075 \cdot 3
\]
**Step 2: Calculate the total amount to be paid back.**
The total amount to be paid back is the loan amount plus the interest:
\[
T = L + I
\]
Now, let's perform the calculations for both problems.
Calculate the value by following steps:
- step0: Calculate:
\(7499\times 0.07\times 3\)
- step1: Multiply the terms:
\(524.93\times 3\)
- step2: Multiply the numbers:
\(1574.79\)
Calculate or simplify the expression \( 78500 * 0.075 * 3 \).
Calculate the value by following steps:
- step0: Calculate:
\(78500\times 0.075\times 3\)
- step1: Multiply the terms:
\(5887.5\times 3\)
- step2: Multiply the numbers:
\(17662.5\)
Calculate or simplify the expression \( 78500 + 17662.5 \).
Calculate the value by following steps:
- step0: Calculate:
\(78500+17662.5\)
- step1: Add the numbers:
\(96162.5\)
Calculate or simplify the expression \( 7499 + 1574.79 \).
Calculate the value by following steps:
- step0: Calculate:
\(7499+1574.79\)
- step1: Add the numbers:
\(9073.79\)
Calculate or simplify the expression \( 9073.79 / 36 \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{9073.79}{36}\)
- step1: Convert the expressions:
\(\frac{\frac{907379}{100}}{36}\)
- step2: Multiply by the reciprocal:
\(\frac{907379}{100}\times \frac{1}{36}\)
- step3: Multiply the fractions:
\(\frac{907379}{100\times 36}\)
- step4: Multiply:
\(\frac{907379}{3600}\)
Calculate or simplify the expression \( 96162.5 / (3 * 12) \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{96162.5}{\left(3\times 12\right)}\)
- step1: Remove the parentheses:
\(\frac{96162.5}{3\times 12}\)
- step2: Multiply the numbers:
\(\frac{96162.5}{36}\)
- step3: Convert the expressions:
\(\frac{\frac{192325}{2}}{36}\)
- step4: Multiply by the reciprocal:
\(\frac{192325}{2}\times \frac{1}{36}\)
- step5: Multiply the fractions:
\(\frac{192325}{2\times 36}\)
- step6: Multiply:
\(\frac{192325}{72}\)
### Solution to Problem 3: Mr. Hassiem's Computer Hire Purchase
1. **Amount Financed:**
\[
A = 8999 - 1500 = 7499
\]
2. **Total Interest Calculation:**
\[
I = 7499 \cdot 0.07 \cdot 3 = 1574.79
\]
3. **Total Amount to be Paid Back:**
\[
T = 7499 + 1574.79 = 9073.79
\]
4. **Monthly Instalment Calculation:**
\[
n = 3 \cdot 12 = 36
\]
\[
M = \frac{9073.79}{36} \approx 252.05
\]
**Final Answer for Problem 3:**
Mr. Hassiem's monthly instalment is approximately **R252.05**.
---
### Solution to Problem 4: Abusiswe's Car Loan
1. **Total Interest Calculation:**
\[
I = 78500 \cdot 0.075 \cdot 3 = 17662.5
\]
2. **Total Amount to be Paid Back:**
\[
T = 78500 + 17662.5 = 96162.5
\]
3. **Monthly Instalment Calculation:**
\[
n = 3 \cdot 12 = 36
\]
\[
M = \frac{96162.5}{36} \approx 2671.18
\]
**Final Answer for Problem 4:**
The total amount Abusiswe has to pay is **R96,162.50**.
Respondido por UpStudy AI y revisado por un tutor profesional

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