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 frontended
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, rule of 78 method, and straight-line method (SLM), we need to have some additional information. Specifically, we need to know the total investment cost and the quarterly installment amount.
However, based on the given information, we can assume the following:
1. Total Investment Cost: Let's assume it is $10,000.
2. Down Payment: The down payment is 20% of the investment cost, so it would be $2,000.
3. Loan Amount: The remaining amount after the down payment would be $8,000.
4. Hire-term: The hire-term is four years, which means there are 16 quarters in total (4 years x 4 quarters).
To calculate the quarterly installment amount, we can use the flat rate of interest. The flat rate of interest is 13%, and it is applied to the loan amount.
Flat interest per quarter = Flat rate of interest * Loan amount / Number of quarters
Flat interest per quarter = 0.13 * $8,000 / 16 = $650
Now, let's calculate the quarterly installment amount:
Quarterly installment amount = (Loan amount + Flat interest per quarter) / Number of quarters
Quarterly installment amount = ($8,000 + $650) / 16 = $531.25
With this information, we can now calculate the interest rebate using the different methods:
(i) Actuarial Method:
The actuarial method calculates the interest rebate based on the actual outstanding balance of the loan.
To calculate the interest rebate using the actuarial method, subtract the remaining principal after 24 quarters (installments) from the original loan amount.
Remaining principal after 24 quarters = Loan amount - (Quarterly installment amount * Number of quarters left)
Remaining principal after 24 quarters = $8,000 - ($531.25 * 12) = $1,625
Interest rebate = Loan amount - Remaining principal after 24 quarters
Interest rebate = $8,000 - $1,625 = $6,375
(ii) Rule of 78 Method:
The rule of 78 method assumes that the interest is distributed evenly over the loan term, so the rebate is calculated based on the unearned interest.
To calculate the interest rebate using the rule of 78 method, use the following formula:
Interest rebate = Total unearned interest * (Number of quarters left / Sum of quarters)
Total unearned interest = (Number of quarters * Quarterly installment amount) - Loan amount
Total unearned interest = (16 * $531.25) - $8,000 = $1,100
Sum of quarters = (Number of quarters * (Number of quarters + 1)) / 2
Sum of quarters = (16 * (16 + 1)) / 2 = 136
Interest rebate = $1,100 * (12 / 136) = $96.32
(iii) Straight-Line Method (SLM):
The straight-line method assumes that the interest is distributed evenly over the loan term, so the rebate is calculated based on the interest paid per quarter.
To calculate the interest rebate using the straight-line method, multiply the quarterly interest amount by the number of quarters left.
Interest per quarter = Flat interest per quarter + (Flat interest per quarter * (Front-ended documentation and service fee + Prompt payment rebate))
Interest per quarter = $650 + ($650 * (0.005 + 0.01)) = $650 + ($650 * 0.015) = $650 + $9.75 = $659.75
Interest rebate = Interest per quarter * Number of quarters left
Interest rebate = $659.75 * 12 = $7,917
Please note that these calculations are based on the assumptions made from the given information.