How to compare the discount rate of a loan with rate of interest?

We may observe that some banks as well as dealers of automobiles and electronic items offer discounted loans to their customers. Discounted loans are the loans that have the interest payment subtracted from the principal before the loan is disbursed.

For example, consider a customer pays Rs.100/- in a year for an item costing Rs.95/-. Here the discount rate is (100-95)/100= 5.00%

In the other words, the annual effective discount rate expresses the amount of interest paid/earned as a percentage of the balance at the end of the (annual) period.

Whereas, the effective rate of interest expresses the amount of interest as a percentage of the balance at the beginning of the period. In the above example, if we have to calculate rate of interest, we shall take Rs.95 as base rate on which Rs.5/- is charged for one year.

(i.e.) the effective interest rate: (100 – 95)/ 95 = 5.26 %

This is in contrast to the effective rate of interest, which expresses the amount of interest as a percentage of the balance at the start of the period.

Normally, banks clarify to their customer that the loan amount is inclusive of Rs. ………., being the discount at …… % per annum for a period of ……….. Months

EMI = [P x R x (1+R) ]/ [(1+R) -1],

Where P is the principal loan amount, R is the Interest rate per month and n is the number of installments.

In an electronic show room it is advertised that the cost of a latest smart TV is Rs.50000/- which is repayable in 10 monthly installments of Rs.5000/- per month. The shopkeeper offers 8% discount if the customer buys the item on full payment. It means the actual cost of the TV set is Rs.46000/- and amount of Rs.50000/- is inclusive of 4000/- being discount at 8% per annum for a period of 10 months.  If XYZ bank offers consumer loan for purchase of television set at interest of 15% p.a. which loan you will prefer between the offer of the show room dealer and the bank?

Here, we will calculate EMI for Rs.46000@15%

EMI = [P x R x (1+R)^n]/ [(1+R)^n-1],

Where P is the principal loan amount, R is the Interest rate per month and n is the number of installments.

EMI@15%=46000×0.0125×(1.0125)^10/(1.0125)^10-1

=46000×0.1025×1.1322÷0.1322=46000×0.0125=4924

Therefore, if you take a loan from the bank  with interest @ 15% EMI works out to Rs.4924 and installments at the shop keeper at 8% discount works out to Rs.5000/-per month. The borrower may prefer bank loan instead of shop keeper’s offers of 10 installments of Rs.5000/- each.