Question

A hire purchase company charges 5% Simple Interest (SI) per annum on goods sold under installment scheme. An article priced Rs.12000 was hire purchased with a down payment of Rs.3000. If the company allows only 12 monthly installments for repayment, find the monthly installment amount to be paid.

Answer 1

Hint:Simple Interest or SI, for a given principal amount $P$ , rate of simple interest $r$ and period of time $t$ is equal to $\dfrac{P\times r\times t}{100}$. The total amount to be paid is equal to the sum of the principal amount and the simple interest. We are asked to find the EMI or Equated Monthly Installments. EMI or Equated Monthly Installments is equal to the total amount to be paid divided by the number of months.

Complete step by step answer:
We are given that an article priced at Rs.12000 was hire purchased with a down payment of Rs.3000. We are also given that the hire purchase company charges 5% Simple Interest (SI) per annum on goods sold.
The amount left to pay after down payment = Total cost of purchase – down payment
=Rs.12000-Rs.3000
=Rs.9000
We are given that the company allows 12 monthly installments for repayment of the amount left, Rs.9000.
But the company charges a simple interest of 5% per annum.
Hence,
The principle amount to be paid, P=Rs.9000
Rate of interest on amount to be paid, r=5% per annum
Time period for repayment, t=12 months=1 year
$\therefore $ Simple interest of the amount to be repaid$=\dfrac{P\times r\times t}{100}$
$=\dfrac{9000\times 5\times 1}{100}$
$=Rs.450$
Hence,
Total amount to be paid in a time period of 12 months= Principle amount +Simple interest
$=Rs.9000+Rs.450$
$=Rs.9450$
We are asked to find the Equated monthly installments. For the same, we divide the total amount by the number of months in which this amount has to be remitted.
Equated monthly installments$=\dfrac{Total\,amount\,to\,be\,paid}{Number\,of\,months}$
$=\dfrac{9450}{12}$
$=Rs.787.5$
Hence, the monthly installment amount to be paid is equal to $Rs.787.5$.

Note:

This question can also be asked when the interest is compound rather than simple.
In that case, use the equation,
Compound interest$=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}$
Where P is the principal amount,
R is the rate of interest,
And n is equal to the total time period divided by the time period of the rate of interest.
This question could also have been asked with the simple interest having a different time period, say 5% per 6 months.
In that case, the total amount to be paid will equal the sum of principal amount added to the simple interest in the first 6 months and principal amount added to the simple interest in the second 6 months. This is simply equal to having a simple interest of 10% per annum.