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 please
To calculate the interest rebate using different methods, we first need to determine the hire-purchase deal's key details. Let's break it down:
Initial investment cost (I) = 100%
Down payment required = 20% of I = 0.2 * I
Remaining financed amount (F) = I - Down Payment = I - 0.2 * I = 0.8 * I
Now, let's calculate the interest payable:
Flat rate of interest = 13%
Number of quarters in the hire term = 4 years * 4 quarters/year = 16 quarters
Interest payable per quarter (IP) = Flat rate of interest / Number of quarters per year
IP = 13% / 4 = 0.13 / 4 = 0.0325 (or 3.25%)
Now, in order to calculate the interest rebate after the 24th installment using different methods, we need to know the total number of installments (N). Since the hire-term is for four years, and payments are done quarterly, we can calculate N as follows:
N = 4 years * 4 quarters/year
N = 16 installments
(i) Actuarial Method:
In the actuarial method, the interest rebate is calculated based on the principle that the rebate is proportional to the remaining financed amount (F).
Interest rebate = F * IP * (N - 24)
(ii) Rule of 78 Method:
In the rule of 78 method, the interest rebate is calculated based on a predetermined schedule. It assumes that the interest payable is spread evenly over all installments.
Interest rebate = F * IP * (N * (N + 1) / 2 - 24 * (24 + 1) / 2)
Interest rebate = F * IP * ((N^2 + N) / 2 - (24^2 + 24) / 2)
(iii) Straight Line Method (SLM):
In the straight-line method, the interest rebate is calculated based on the remaining financed amount (F) and the percentage-fee rebate rate.
Interest rebate = F * Rebate rate * (N - 24)
Now, to find the exact interest rebate values, we need the values of I, N, and rebate rates for the front-ended documentation and service fee. Please provide these values, and I will calculate the interest rebate according to each method for you.