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CAT Compound Interest: Relation Among Principal, Time, Rate Percent of Interest Per Annum and Total Interest - Practice Questions & MCQ

Edited By admin | Updated on Oct 05, 2023 05:01 PM | #CAT

Quick Facts

  • 5 Questions around this concept.

Solve by difficulty

Find the compound interest earned on Rs. 20000 for 2 years at 10% p.a. the interest being compounded annually.

The interest on a certain sum lent at compound interest, the interest being compounded annually, in the 2nd year is Rs.1200. The interest on it in the 3rd year is Rs. 1440. Find the rate of interest per annum.

A certain loan amount, under compound interest, compounded annually earns an interest of Rs. 1980 in the second year and Rs. 2178 in the third year. How much interest did it earn in the first year?

Concepts Covered - 1

Compound Interest: Relation Among Principal, Time, Rate Percent of Interest Per Annum and Total Interest

Definition: Compound Interest (CI) refers to the interest that accumulates on both the initial principal and the accumulated interest from previous periods.

Formula: 

\mathrm{A=P\left(1+\frac{R}{100}\right)^T}

Where,

A = Total amount after T years

P = Principal (initial amount)

R = Rate of interest per annum (in %)

T = Time period (in years)

The Compound Interest (CI) is given by:

\mathrm{CI=A-P}

Tip 1: Always be clear about the compounding frequency - annually, semi-annually, quarterly, or monthly. Adjust the rate and time accordingly. If compounding is semi-annually, divide R by 2 and multiply T by 2.

Foundation Building Questions:

Question: A sum of ₹10,000 is invested at 10% per annum compounded annually. What will be the amount after 3 years?

Solution: 

Using the formula:

\mathrm{\begin{gathered} \mathrm{A}=P\left(1+\frac{R}{100}\right)^T \\ \mathrm{A}=10,000\left(1+\frac{10}{100}\right)^3 \\ \mathrm{A}=10,000(1.1)^3 \\ \mathrm{A}=13,310 \end{gathered}}

So, the amount after 3 years will be ₹13,310.

Tip 2: To quickly calculate CI for two years at rate R%, use the formula:

\CI = P \times R% \times (1 + R%) \

This is particularly handy for quick calculations and objective exams.

Tip 3: When dealing with multiple compounding periods in a year, always adjust the time and rate. For example, for quarterly compounding over 2 years at 8% p.a., R becomes 2% (i.e., 8/4) and T becomes 8 (i.e., 2 X 4).

Application of Previous Concept (Simple Interest)

Remember that for the first year, Simple Interest and Compound Interest are the same. This understanding can help speed up calculations for certain problems.

Example:

Question: An amount of ₹15,000 is lent out at a compound interest rate of 6% per annum compounded semi-annually. What is the interest earned after 2 years?

Solution:

First, adjust for semi-annual compounding:

\mathrm{R = 6/2 = 3% and T = 2 \times 2 = 4.}

Using the CI formula:

\mathrm{\begin{gathered} \mathrm{A}=P\left(1+\frac{R}{100}\right)^T \\ \mathrm{~A}=15,000\left(1+\frac{3}{100}\right)^4 \\ \mathrm{~A}=16,813.81 \end{gathered}}

CI = A - P

CI = ₹16,813.81 - ₹15,000 

= ₹1,813.81 

Interest earned is ₹1,813.81.

Tip 4: In questions involving both SI and CI, compute the SI for the entire period first. Then, calculate the CI for the period minus the SI to find the additional interest due to compounding.

By continually practising, not only do you familiarise yourself with the formulas, but you also develop shortcuts and strategies to tackle any kind of problem on this topic in management entrance exams.

 

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