CAT Problems on instalments - Practice Questions & MCQ

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1 Questions around this concept.

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A person deposited a certain amount in a bank which is offering 10% p.a. compound interest for the first two years and for the next two years, each year the rate of interest is 10% points more than the previous year. The value of his investment at the end of the 3rd year is Rs. 4840 more than that at the end of the second year. Find the total amount received by the person at the end of the 4^thyear.

Rs. 37752

Rs. 38572

Rs. 38752

Cannot be determined

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Concepts Covered - 1

Problems on instalments

Instalments refer to the periodic payments made to settle a debt. They are prevalent in various financial scenarios like buying a house, car, or any other high-value item on credit. This concept can be understood using both Simple and Compound Interest principles.

1. Using Simple Interest (SI)

For equated monthly instalments (EMIs) with Simple Interest, the interest is calculated on the original principal throughout the loan period.

Formula:

$\mathrm{E M I=\frac{P+(P \times R \times T)}{n}}$

Where:

- P = Principal amount

- R = Rate of interest per annum

- T = Time in years

- n = Number of instalments

2. Using Compound Interest (CI)

For EMIs with Compound Interest, the interest is calculated on the reducing balance every month.

Formula:

Where:

- P = Principal amount

- r = Monthly rate of interest (annual rate divided by 12)

- n = Number of instalments

Foundation Building Questions (Example with SI) :

Question: A person takes a loan of ₹50,000 at a simple interest rate of 12% per annum and agrees to repay in 10 equal monthly instalments. Find the EMI.

Solution:

Using the SI formula:

$\mathrm{\begin{gathered} E M I=\frac{P+(P \times R \times T)}{n} \\ E M I=\frac{50,000+\left(50,000 \times 12 \times \frac{10}{12 \times 100}\right)}{10} \end{gathered}}$

EMI = ₹5,500

Tips and Tricks:

Tip 1: Determine whether the interest is Simple or Compound before proceeding.

Tip 2: Always convert the annual interest rate to monthly if calculating monthly instalments (divide by 12).

Tip 3: If there's any down payment, subtract that from the principal before calculating the EMI.

Application of Previous Concepts (Simple & Compound Interest):

EMI calculations are direct applications of the principles of SI and CI. You are essentially spreading out the total repayable amount (principal plus interest) over a series of periodic payments.

Solved Example (Example with CI):

Question: A man takes a car loan of ₹3,00,000 at 12% per annum compounded monthly. He agrees to repay it in 24 equal monthly instalments. Find the EMI.

Solution:

Using the CI formula:

$\mathrm{r=\frac{12}{12\times100}=0.01}$

n = 24

$\mathrm{\begin{gathered} E M I=\frac{3,00,000 \times 0.01 \times(1+0.01)^{24}}{(1+0.01)^{24}-1} \\ E M I \approx 14,117.39 \end{gathered}}$

Tip 4: Round off the EMI to the nearest rupee as it represents a real-world monetary value.

Understanding EMIs and their calculation is not just crucial for exams but also for real-life applications. Regular practice with previous year questions will ensure the students' proficiency in this important concept, and remembering the tips will help them approach these problems with ease.