Question 1194189: Rose wants to buy a car on hire purchase for N$75,000.00 at the rate of 11% p.a. repayable using monthly installments for a period of 3 years and 10 months. (No deposit was required). Use the given information to calculate the:
(a) Total amount of money expected to be paid to the Hire Purchase Company over the years. (5)
(b) Monthly installment to be paid by Rose. (5)
c) Bank 1 offered her a loan repayable at a certain monthly installment for the same period of time as the car hire company at the rate same rate of 11% p.a. whereas Bank 2 offered to reduce the rate of by 1.5% p.a. What is the:
(i) Total amount of money expected to be received by Bank 1. (5)
(ii) Monthly instalment to be paid by Rose to Bank 1. (5)
(iii) Total amount of money expected to be received by Bank 2 using the reduced interest rate. (5)
(iv) Monthly installment to be paid by Rose to Bank 2. (5)
(v) How much money will Rose save per month using the cheapest option?
Answer by parmen(42)   (Show Source):
You can put this solution on YOUR website! **a) Total Amount of Money Expected to be Paid to the Hire Purchase Company**
* **Calculate Total Repayment Period in Months:**
- 3 years * 12 months/year + 10 months = 46 months
* **Calculate Total Interest:**
- **Annual Interest:** N$75,000 * 11% = N$8,250
- **Total Interest (Approximate):** N$8,250 * (46/12) = N$31,625
* **Total Amount to be Paid:**
- Car Price + Total Interest = N$75,000 + N$31,625 = N$106,625
**b) Monthly Installment**
* **Monthly Installment:** Total Amount to be Paid / Number of Months
- N$106,625 / 46 = N$2,318.37 (approximately)
**c) Bank 1 Calculations**
* **(i) Total Amount of Money Expected to be Received by Bank 1:**
- This would be the same as the car price: N$75,000
* **(ii) Monthly Installment to Bank 1:**
- This requires using a loan amortization formula or a financial calculator.
- **Note:** The exact formula and its application may vary slightly depending on the specific compounding method used by the bank.
- **General Approach:**
- Use the loan amortization formula to calculate the monthly payment based on the loan amount (N$75,000), interest rate (11% p.a.), and loan term (46 months).
* **(iii) Total Amount of Money Expected to be Received by Bank 2:**
- Same as Bank 1: N$75,000
**c) Bank 2 Calculations**
* **(iv) Monthly Installment to Bank 2:**
- Use the loan amortization formula with the reduced interest rate (11% - 1.5% = 9.5% p.a.), loan amount (N$75,000), and loan term (46 months).
**c) (v) Savings per Month**
* **Calculate the difference in monthly installments:**
- Monthly Installment to Bank 1 - Monthly Installment to Bank 2
**Important Notes:**
* **Loan Amortization Formula:** This formula calculates the equal periodic payment required to pay off a loan over a specific term. It considers the principal amount, interest rate, and number of periods.
* **Financial Calculators:** Many financial calculators (or online calculators) can directly compute loan payments based on the given inputs.
* **Rounding:** Ensure proper rounding throughout the calculations to avoid significant discrepancies in the final results.
**Disclaimer:** This information is for general guidance only and may not constitute financial advice. It's crucial to consult with a financial professional for personalized and accurate calculations based on your specific circumstances and the terms and conditions of the loan agreements.
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