The hypothetical finance ltd has structured a hire-purchase deal.The required to make a down payment of 20 percent of the investment cost.The hire term is four years with quarterly payment in advance . The flat rate of interest is 13 percent. The finance company would charge a front-ended documentation and service fee and rebate for prompt payment@ 0.5 percent and 1 percent 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) rupe of 78 method and. (iii) SLM

To calculate the interest rebate in different methods, we need to understand the terms and calculations involved in each method.

(i) Actuarial Method:
In the actuarial method, interest is calculated based on the reducing balance principle. Here are the steps to calculate the interest rebate using the actuarial method:

1. Calculate the initial investment cost:
Multiply the investment cost by (100% - down payment percentage) to get the initial investment cost. In this case, it would be 80% of the investment cost.

2. Calculate the quarterly installment amount:
Divide the initial investment cost by (hire term in years * number of installments per year) to get the quarterly installment amount. Since there are 4 years and quarterly payments, the number of installments per year would be 4.

3. Calculate the total interest paid:
Multiply the quarterly installment amount by the total number of installments (24 in this case). This will give you the total amount paid as installments.

4. Calculate the interest rebate:
Multiply the total interest paid by the rebate percentage for prompt payment (1% in this case).

5. Subtract the interest rebate from the total interest paid to get the final interest rebate.

(ii) Rule of 78 Method:
The Rule of 78 is a method used to calculate interest rebates based on the assumption that the principal paid over time follows a predetermined pattern. Here are the steps to calculate the interest rebate using the Rule of 78 method:

1. Calculate the sum of digits:
Add the digits from 1 to the hire term (4 in this case). The sum of digits will be 10.

2. Calculate the interest rebate ratio:
Divide the remaining number of installments (24 - 24 = 0 in this case) by the sum of digits (10). The interest rebate ratio would be 0/10 = 0.

3. Calculate the interest rebate:
Multiply the total interest paid by the interest rebate ratio (0 in this case).

(iii) Straight Line Method (SLM):
The Straight Line Method calculates the interest rebate by simply dividing the total interest paid by the hire term. Here are the steps to calculate the interest rebate using the SLM:

1. Calculate the total interest paid (same as in the actuarial method).

2. Divide the total interest paid by the hire term (4 years) to get the interest rebate.

By following these steps for each method, you can calculate the interest rebate according to the actuarial method, the Rule of 78 method, and the Straight Line Method (SLM).