The Hypothetical Finance Ltd has structured a hire-purchase deal. The required to make a down payment of 20 per cent of the investment cost. The hire-term is four years with quarterly payment in advance. The flat rate of interest is 13 per cent. The finance company would charge a front- ended documentation and service fee and allow rebate for prompt payment @ 0.5 per cent and 1 per cent of investment outlay respectively.

Assuming after paying 24th installment, a hirer wishes the purchase option, what is the interest rebate according to (i) actuarial method, (ii) rule of 78 method and, (iii) SLM?

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The Hypothetical Finance Ltd has structured a hire-purchase deal. The required to make a down payment of 20 per cent of the investment cost. The hire-term is four years with quarterly payment in advance. The flat rate of interest is 13 per cent. The finance company would charge a front- ended documentation and service fee and allow rebate for prompt payment @ 0.5 per cent and 1 per cent of investment outlay respectively.

Assuming after paying 24th installment, a hirer wishes the purchase option, what is the interest rebate according to (i) actuarial method, (ii) rule of 78 method and, (iii) SLM?

To calculate the interest rebate using the actuarial method, the rule of 78 method, and the SLM (Straight Line Method), we need to understand the terms and calculations involved.

Here are the steps to calculate the interest rebate using each method:

1. Actuarial Method:
- Determine the total hire-purchase cost by subtracting the down payment from the investment cost.
- Calculate the amount borrowed by dividing the total hire-purchase cost by (1 + interest rate).
- Determine the interest paid by subtracting the borrowed amount from the total hire-purchase cost.
- Calculate the interest paid per quarter by dividing the total interest paid by the number of quarters.
- Multiply the interest paid per quarter by the number of remaining quarters after the 24th installment.
- Calculate the interest rebate by multiplying the result from the previous step by the prompt payment rebate rate.

2. Rule of 78 Method (Sum of Digits):
- Determine the total hire-purchase cost by subtracting the down payment from the investment cost.
- Calculate the interest portion of each installment by multiplying the total interest paid (total hire-purchase cost * interest rate) by the fraction of remaining quarters.
- Multiply the interest portion of each installment by the number of remaining quarters after the 24th installment.
- Calculate the interest rebate by multiplying the result from the previous step by the prompt payment rebate rate.

3. SLM (Straight Line Method):
- Determine the total hire-purchase cost by subtracting the down payment from the investment cost.
- Calculate the interest paid per quarter by dividing the total interest paid (total hire-purchase cost * interest rate) by the total number of quarters.
- Multiply the interest paid per quarter by the number of remaining quarters after the 24th installment.
- Calculate the interest rebate by multiplying the result from the previous step by the prompt payment rebate rate.

By following these steps, you can calculate the interest rebate using the actuarial method, the rule of 78 method, and the SLM for the given hire-purchase deal.