chapter 5

BUSINESS AND CONSUMER CREDIT

Items like electrical appliances can either be purchased on cash term or instalment basis. In an instalment purchase, a down payment is made followed by a series of regular payments (usually monthly or weekly).

There are many retailers and wholesalers who sell their products on an instalment basis. You can buy an electrical item by paying a number of weekly or monthly instalments. When you are an instalment buyer, you are actually paying more than the cash price. The difference is the interest you have to pay for the credit given to you by the seller (unpaid balance), plus insurance and finance charges.

All hire purchase sales in Malaysia are controlled by the Hire-Purchase Act 1967. Ht eHire-Purchase Act states that interest rates charged should not be more than 10% per annum on a flat rate basis.

Interest charge based on original balance

In an istalment purchase, when interest charge is based on the original balance, the simple interest formula is used to calculate interest. Several expressions such as charge based on original unpaid balance charge based on simple interest rate and charge based on flat rate are common used in instalment purchases but they all mean the same thing.

Normally, an instalment purchase requires a down payment. The original balance is given by

Original balance = cash price – down payment

The total amount paid in an instalment plan by the buyer is called instalment price; that is,

Instalment price = cash price + total interest

OR

Instalment price = Down payment + total monthly payment

The monthly payment can be calculated by dividing the sum of the sum of the original balance and interest by the number of instalments; that is,

Monthly payment = Original balance + Total interest

Number of payments







Example

Elfreeda bought a refrigerator listed at RM800 cash through an instalment plan. She paid RM100 as a down payment. The balance was settled by making ten monthly instalment. If the interest rate charged was 8.5% per annum on the original balance, find

a. The total interest charged
b. The instalment price
c. The monthly payment

Example

Elfeera bought an electric appliance through an instalment plan in which she paid RM200 down. She had to make 12 monthly payments of RM120 each to settle the unpaid balance. If the dealer charged her an interest of 5% per annum on the original balance, find the cash price of the item.

































Interest charge based on reducing balance

As opposed to simple interest rate, interest rate charged on reducing balance is an annual rate which is applied only to the balance due at the time of each payment. There are several methods to calculate interest charge based on the reducing balance. The annual rate based on annuity method is the effective rate. Other rates that are based on reducing balances are not effective rates but may be close approximations of the effective rate.

In this section, we shall discuss only two methods of reducing balance, namely

• Annuity method
• Constant ratio formula

Annuity method

The annuity method is also called the amortization method. The Federal government in providing housing loans uses this method to compute the monthly instalments. Many banks also use this method of calculation but with some variations. Usually, the banks first determine the annual payment using the annual rest (interest rate) and then divide the annual payment by 12 to arrive at the monthly instalment.

If A is the amount of loan borrowed, i is the interest rate per interest period and n the number of interest periods or the number of instalment repayments, then

A = R 1 – (1 + i) –n

i

where R is the instalment payment for each period. Solving for R, we get

A = R Ai

1 – (1 + i) –n

Thus, if the amount of the loan A, interest rate i, and the number of instalments are known, the amount of the instalment payment can be calculated. The formula also allows us to find the amount of the original loan if the interest rate, instalment payment and the number of instalments are known.

Example

A washing machine is selling for RM2000 cash. Through an instalment purchase, the buyer has to pay RM400 down and ten monthly instalments. If the interest charged is 8% per annum on reducing balance, find

a. The monthly payment

b. The total interest charged

c. The instalment price

by using the annuity method

Constant Ratio formula

The Constant Ratio formula is frequently used to approximate the actual annual percentage rate, APR or effective rate.

The constant ratio formula is given by

r = 2MI

B (n + 1)

Where

r = annual interest rate

M = 12 monthly instalments and 52 form weekly instalments

I = total interest charged for instalment plan

B = original outstanding balance or principal of original debt

n = total number of instalments

The constant ratio formula can also be used to calculate the total interest charged if the interest rate on the reducing balance is given, that is,

I = B (n + 1) r

2n

The formula is derived as follows

Let

The original outstanding balance = B ringgit

Number of partial payments to settle the balance = n

Total interest charged = I

Annual interest rate charged = r%

Number of repayments in a year = m











Example

A washing machine is being sold for RM2000 cash. The buyer has to pay RM400 as down payment and 10 monthly instalments. If the interest charged is 8% per annum on the reducing balance, find

a. The total interest charged

b. The monthly payment

c. The instalment price

by using the Constant Ratio formula



Example

Darwisya purchased a RM8000 piano through an instalment plan. She has to pay RM2000 as down payment and 18 monthly payments of RM350 each. Find the

a. Instalment price

b. Total interest charged

c. Flat rate (simple interest rate) charged

d. Approximate APR by using the Constant Ratio formula



Example

Harisya purchased RM4000 computer. He has to pay RM2000 as down payment and 20 weekly payments of RM110 each. Find the approximate effective rate that is charged by using the Constant Ratio Formula.



Example

An electric guitar is priced at RM300 cash. A cash purchase is entitled to a 10% discount. The guitar can be purchased for RM50 as down payment and RM13 a week for 20 weeks. Find the approximate effective rate charged to the instalment buyer by using the Constant Ratio Formula