1. 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?
answer briefly

To calculate the interest rebate using different methods, let's break down the information provided:

1. Down Payment: 20% of the investment cost.
2. Hire-term: Four years with quarterly payments in advance.
3. Flat rate of interest: 13%.
4. Front-end documentation and service fee.
5. Rebate for prompt payment: 0.5% and 1% of investment outlay.

To find the interest rebate using different methods, we need to calculate the total interest paid until the 24th installment.

(i) Actuarial Method:
In the actuarial method, the total interest paid is calculated based on the remaining balance after each installment payment. Here's how to find the interest rebate:

1. Calculate the initial investment cost: Subtract the down payment (20%) from the total cost.
2. Calculate the quarterly installment: Divide the remaining investment by the number of installments (4 years x 4 quarters = 16).
3. Calculate the interest paid per quarter: Multiply the quarterly installment by the interest rate (13% / 4).
4. Calculate the total interest paid after 24 installments: Multiply the interest paid per quarter by 24.
5. Calculate the interest rebate: Subtract the total interest paid after 24 installments from the interest paid until the 24th installment.

(ii) Rule of 78 Method:
The Rule of 78 method assumes that interest is paid in a decreasing pattern over the loan term. Here's how to find the interest rebate:

1. Calculate the sum of digits: Add the digits from 1 to 24 (1+2+3+...+24).
2. Calculate the interest paid for each installment: Divide the total interest by the sum of digits.
3. Calculate the total interest paid after 24 installments: Multiply the interest paid for each installment by 24.
4. Calculate the interest rebate: Subtract the total interest paid after 24 installments from the interest paid until the 24th installment.

(iii) Straight Line Method (SLM):
In the straight-line method, equal amounts of interest are paid per installment over the loan term. Here's how to find the interest rebate:

1. Calculate the total interest paid per installment: Divide the remaining investment by the number of installments (24).
2. Calculate the total interest paid after 24 installments: Multiply the interest paid per installment by 24.
3. Calculate the interest rebate: Subtract the total interest paid after 24 installments from the interest paid until the 24th installment.

Remember to factor in any prompt payment rebates, front-end fees, and other terms and conditions mentioned in the agreement to get an accurate calculation of the interest rebate.