Question

The cost of a motor bike is Rs. 48,000. The company offers it in 30 months of equal instalments at 10% rate of interest. Find the equated monthly instalment.

Answer 1

Hint: Equated monthly instalment is also known as EMI. They are similar to loans that banks provide with some interest that the borrower has to give to the loan provided. Use the formula for EMI and find the EMI for the given data.

Complete step by step answer:
Let us first understand what is meant by equated monthly instalment, before we calculate the equated monthly instalment for the given data.
Equated monthly instalment is also known as EMI. They are similar to loans that bank provide with some interest that the borrower has to give to the loan provided.
We can say that EMI is a loan that a company offers when we go to buy a product of that company. However, this loan is not in the form of money. Rather the company gives us the product that we want and deals with us that we do not have to pay the full amount at once and can pay some fixed amount every month for a certain amount of time. However, some amount of interest is also included in the total amount that has to be paid.
The formula for EMI is as follows:
$EMI=P\times r\times \dfrac{{{(1+r)}^{n}}}{{{(1+r)}^{n}}-1}$ …. (i)
Here, P is called principal amount. It is the actual price of the product.
r is the rate of interest.
n is the number of months for which the EMI has to be paid.
It is given that $P=48000$, $n=30$ and $r=10%=0.1$.
Substitute these values in (i).
$\Rightarrow EMI=48000\times (0.1)\times \dfrac{{{(1+0.1)}^{30}}}{{{(1+0.1)}^{30}}-1}$
$\Rightarrow EMI=4800\times \dfrac{{{(1.1)}^{30}}}{{{(1.1)}^{30}}-1}=1815$
Therefore, the EMI for the bike is Rs. 1815

Note: Most of the times students forget to convert the rate of interest from percentage into decimal. Therefore, students must be careful in this.
You may think that EMI is a very good option to buy most of the product. However, it is not a good option for every product.
In the above case, the EMI is Rs. 1815 to be paid for 30 months. This means that the man pays a total amount of $1815\times 30=54450$ (in rupees). However, the market price of the bike is Rs. 48000.
This means that you end up paying a lot of interest.