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 options, what is the interest rebate according to (i) actuarial method, (ii) rule of 78 method and, (iii) SLM?
To calculate the interest rebate for the given hire-purchase deal, we need to understand the three methods mentioned: the actuarial method, the rule of 78 method, and the SLM (Straight Line Method).
(i) Actuarial Method:
In the actuarial method, the interest rebate is calculated by considering the reduced balance outstanding after the 24th installment. The interest rebate is based on the difference between the flat rate of interest and the effective interest rate.
To calculate the interest rebate using the actuarial method, follow these steps:
Step 1: Calculate the quarterly installment amount.
First, calculate the value of the periodic payment (quarterly installment).
Let's assume the investment cost is C.
The down payment is 20% of C, which means the financed amount is 80% of C.
Quarterly installment amount = (Financed amount * Flat rate of interest) / (1 - (1 + Flat rate of interest)^(-total number of quarters))
Step 2: Calculate the reduced balance outstanding after the 24th installment.
The reduced balance outstanding after the 24th installment can be found using the formula:
Reduced balance = (Quarterly installment amount * (1 - (1 + Flat rate of interest)^(-remaining number of quarters))) / Flat rate of interest
Step 3: Calculate the interest rebate.
The interest rebate using the actuarial method is the difference between the total interest paid and the reduced balance.
Total interest paid = (Quarterly installment amount * (total number of quarters)) - Financed amount
Interest rebate = Total interest paid - Reduced balance
(ii) Rule of 78 Method:
The rule of 78 method (also known as the sum-of-digits method) assigns higher weightage to the earlier installments. It assumes that the rebate is proportional to the sum of the digits of the remaining installments.
To calculate the interest rebate using the rule of 78 method, follow these steps:
Step 1: Calculate the sum of the digits.
The sum of the digits can be found by adding all the digits from 1 to the total number of quarters.
Step 2: Calculate the rebate ratio.
The rebate ratio is the proportion of the remaining quarters to the sum of the digits.
Rebate ratio = (Remaining number of quarters) / (Sum of the digits)
Step 3: Calculate the interest rebate.
The interest rebate using the rule of 78 method is the rebate ratio multiplied by the total interest paid.
Total interest paid = (Quarterly installment amount * (total number of quarters)) - Financed amount
Interest rebate = Rebate ratio * Total interest paid
(iii) SLM (Straight Line Method):
The Straight Line Method assumes an equal distribution of the rebate over the remaining installments. It calculates the rebate based on the ratio of the remaining quarters to the total number of quarters.
To calculate the interest rebate using the SLM, follow these steps:
Step 1: Calculate the rebate ratio.
The rebate ratio is the proportion of the remaining quarters to the total number of quarters.
Rebate ratio = (Remaining number of quarters) / (Total number of quarters)
Step 2: Calculate the interest rebate.
The interest rebate using the SLM is the rebate ratio multiplied by the total interest paid.
Total interest paid = (Quarterly installment amount * (total number of quarters)) - Financed amount
Interest rebate = Rebate ratio * Total interest paid
By using these methods, you can calculate the interest rebate for the given hire-purchase deal after paying the 24th installment.