1. Instalments – An Introduction

#1.

A typical scenario is when products are bought by a small down-payment and the balance amount is paid through a series of payment (usually equal amounts), at regular intervals (usually monthly). This series of equal monthly payments is called Instalments or more specifically EMIs (equated monthly instalments).

A similar situation is also when a business borrows a large sum of money as loan and the loan is repaid through instalments, where the instalments can be paid quarterly or even annually. One can even equate the purchase of a product at EMIs as taking a loan equal to the price of the product and then repaying it through instalments.

As a cost of using the product without having paid fully for it, or in other words, for taking a loan, one has to pay interest charges. The rate at which the interest is charged, and also the duration over which the instalments will be paid to replay the entire loan, is negotiated between the two parties at the outset.

#2.

The terms of interest to us are:

i. The loan taken, expressed in Rs., denoted as P (for Principal),

If some down-payment has to be made, P = Price − Down-payment.

ii. The rate of interest being charged, expressed in % for a specific period, denoted as r%

If it is a case of monthly instalments, use r% p.m.; if it is a case of annual instalments, use r% p.a.; is usually not used, but if it is a case of quaterly instalments, use r% p.q.

To convert a rate from ‘per annum’ to ‘per month’, just divide by 12. Conversely to convert a ‘per month’ rate to ‘per annum’, multiply by 12.

And needless to say, also important is whether it is a case of Simple Interest or Compound Interest. If nothing is mentioned in the question, consider it as a case of Simple Interest.

The loan amount (P), the rate of interest (r%) and the number of instalments (n) all together decide the instalment amount or the EMI. Even if the frequency of paying instalments is annual, we will still call it as EMIs, and will not break a sweat over the ‘monthly’ word in EMIs. Next two lessons give the formula to find the EMI using these terms as input.

#3.

The following two scenarios are different:

“I owing someone Rs. 1,00,000 today” and ” I owing someone Rs. 1,00,000, to be paid after 3 years”.

Even though the amount owed, Rs. 1,00,000, is the same, in the former case this value has to be paid today; whereas in the latter case, this Rs. 1,00,000 has to be paid after 3 years.

The latter case i.e. a given value is due at some future date, in questions, is worded as ‘I owe a debt of Rs. 1,00,000 due in 3 years’. Now, we have one more term ….

Debt, expressed in Rs, denoted as D, is a value that is owed at some future date.

Instead of waiting entire 3 years and then paying Rs. 1,00,000, I might choose to “discharge the debt” by making instalment like payments at end of each successive year, for the next 3 years, such that by the end of 3 years, I have cleared my debt in total. And if I do this, it becomes a question of instalments.

Since I am paying some part of the debt even before it is become due, I need to gain something in doing this. It is same like me ‘lending’ it to the other party before time. So, I should be earning some interest for having given part of the money before time. Or you could just think as … I deposit Rs. X in a bank at end of year 1, which starts earning me some interest. I deposit another Rs. X at end of 2nd year, which will earn me interest on this part hereafter. At end of 3rd year, I add another third instalment of Rs. X from my pocket, and also close the above two accounts, withdraw the amounts (including interest earned) and , and pay all this money to whoever I owed the Rs. 1,00,000. Since the sum, 3X + Interest = 1,00,000, one should notice that the instalment amount X is actually less than just 1,00,000/3, because of the interest that I earn.

The difference between the terms P and D is a important distinction worth noting, because it will change the formula or expression used to solve.