# Math's: Instalment Buying: Meaning and Important Terms and Finding Interest in Instalment Plan

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## Instalment Buying – Meaning and Important Terms

Instalment Buying is a scheme that enables a person to buy costly goods, on convenient terms of payment. Under the scheme, a fixed amount is paid at the time of purchase and the rest of the amount is to be paid in instalments, which may be monthly, quarterly, half yearly or yearly, as per the agreement signed between the customer and the seller. Example- Mr. A bought a car of ₹150,000 by paying ₹50,000 at the time of purchase and the balance in easy instalments.

• Cash Price: The cash price of an article is the amount which a customer has to pay in full for the article at the time of purchase.

• Cash Down Payment: The amount to be paid (in cash) under an instalment plan at the time of purchase of a commodity, is called the cash down payment. It is the partial payment made by the customer at the time of signing the agreement and taking away the article for use.

• Instalments: It is the amount which is paid by the customer at regular intervals towards the remaining part of the selling price of the article.

• Interest under the Instalment Plan: Under Instalment Buying, the seller charges some extra amount for deferred payments. This extra amount is actually the interest charged on the amount of money which the customer owes to the seller at different times of payment of instalments.

## Finding Interest in an Instalment Plan

Example- A truck is sold for ₹100000 cash or for ₹25000 as cash down

payment followed by payment of ₹90000 after one year. Find the rate of interest charged under the instalment plan.

Sol- Cash Price of the truck

Cash down payment

Balance to be paid

Interest

Rate of Interest

## Finding the Amount of Instalment

Example- A scooty is available for ₹45000 cash or for ₹15000 cash down payment and 3 equal monthly instalments. If the rate of interest charged under the instalment plan is 25%. Find the amount of each instalment.

Sol- Cash price of scooty

Cash down payment

Let each instalment

∴ Amount paid in instalment plan

∴ Interest payable

The buyer owes to the seller for first month

The buyer owes to the seller for 2nd month

The buyer owes to the seller for 3rd month

∴ Total principal for on which the interest is to be paid

Rate of interest

Amount of each instalment

## Finding the Cash Price

Example - A TV Set was purchased by paying ₹3600 as cash down payment followed by three equal monthly instalments of ₹3900 each. If the rate of interest charged under instalment plan is 16% p.a., find the cash price of the TV set.

Sol- Let the cash price of the TV set be ₹x

Cash down payment

Amount paid in 3 instalments

Total paid

∴ Interest payable

Principal for 1st month

Principal for 2nd month

Principal for 3rd month

Total principal on which interest is payable

Thus, the cash price of TV set .

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