Calculation of Hire Purchase Loan

Hire purchase loan is a contract which the buyer become the hirer and the bank or financier financing the goods (example: car) become the owner. You’ll be paying installment to the bank for duration as agreed in the contract, while you’ll have the possession of the car, not the ownership. As soon you have finish paying all installment, the ownership will be transferred to you.

The concept is, you be renting the car from the financier, at the end of the contract you’ll buying back the car at a predetermined price. In reality when you pay your installment it is considered as covering for the rental as well the predetermine price paid by installment. 

(Note: Islamic loan use the same method of calculation as hire purchase loan)

How they calculate the interest?

Loan amount × Interest × Number of years = Total Interest

How to calculate the monthly installment?

(Loan amount + Interest) ÷ Number of months = Your monthly installment

Let’s look at an example.

Mr. Ali Babu Cheng (aka Mr. ABC) bought a brand new car for $55,000. He used $5,000 from his savings for the car down payment. He took a hire purchase loan from Iwantyourmoney Bank (aka IWYM Bank) for the balance $50,000. IWYM Bank charge an interest of 5% and the loan tenure is 5 years.

Total Interest = $ 50,000 × 5% × 5 years
= $ 12,500 (Total interest charged)

Monthly Installment = ($ 50,000 + $ 12,500) ÷ 60 months
= $ 1041.67 (The amount Mr. ABC have to fork out every month)

Every month when you make payment, part of the installment will be used to pay interest and another part to settle the principal amount. So, next question my fellow students, what is the amount of interest paid for the 1^st year by Mr. ABC?

Most people might calculate this way,

Total interest ÷ 5 years = Yearly interest charged

So, the interest paid by Mr. ABC for the 1^st year is, $12,500 ÷ 5 = $ 2,500 and interest portion paid per month, $2,500 ÷ 12 = $208.33

That’s what a lot of people think, but the truth is its totally wrong.
Get ready, it’s rather complicated. Here is how it’s calculated,

Step 1:

Add all number from1 until number of ‘Total months’. Let’s call it sum of months.

Example:
Total months= 60
Add all the numbers from 1 to 60.

60+59+58+57+56+…….+5+4+3+2+1=1830 (Sum of months)

The short cut to calculate this is,

(Total months + 1) × (Total months ÷ 2) = Sum of all number from 1 to ‘Total Months’

The same example by using the short cut,
(60+1) × (60 ÷ 2) = 1830 (Sum of months)

Step 2:

((Total month + 1) – N^th month) ÷ ‘Sum of months’ × Total Interest charged = Interest portion for Nth month.

Example:

For 1^st month of payment, the interest portion is:

((60+1) – 1)÷ 1830) × $12,500
= 60$ 409.836.

For 32^nd month of payment, the interest portion is:

((60+1) – 32) ÷ 1830) × $12,500 = $ 198.09

Step 3:

Now to find the 1st year interest paid by Mr. ABC’s on his loan, add interest portion from month 1 to month 12.

(60+59+58+57+56+55+54+53+52+51+50+49) ÷ Sum of months × Total Interest
= Interest for first year.

So,
654 ÷ 1830 × $12,500 = $4,467

That’s 35.7% of your total interest.

As you can see, instead of paying the interest equally, you are paying the most in the first year.

What is rebate?

When you have paid fully earlier or would like to settle earlier, you’ll be given a rebate on your interest. Don’t think that you have some discounts on your interest. It’s just a term without any value used to calculate the balance you have to settle. Let me explain in the below example.

Mr. Dhandhum took a hire purchase loan of $50,000 to buy a car. He took it for 5 years with an interest of 5%. He planned to settle the loan within 3 years. At the end of 3rd year, he decided to settle his loan. What would be his total rebate? How much balance he has to pay?

His total loan is $62,500 including interest.
At end of 3rd year, his rebate would be his unpaid interest portion.
So his total rebate = Interest for year 4 and year 5.
= $1,516 + $533
= $2,049

Balance to settle loan = Total loan with interest – Total installment paid – Total rebate
= $62,500 – ($1041.67 × 36 months) – $2,049
= $62,500 – $37,500.12 – $2,049
= $22,980.88

Did you notice something? If you pay your 5 years loan in 3 years, the total interest paid is higher than a 3 year loan.

Source: moneyburp.blogspot.com