Interests - Quant/Math - CAT 2009
Question 4 the day:
June 5, 2002
The question for the day is from the topic of compound interest.
- What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?
| (1) | 2400 | | (2) | 2592 | | (3) | 2678 | | (4) | 2540 |
Correct Answer - (2)
Solution:
The usual way to find the compound interest is given by the formula A =  .
In this formula, A is the amount at the end of the period of investment
P is the principal that is invested
r is the rate of interest in % p.a
And n is the number of years for which the principal has been invested.
In this case, it would turn out to be A = 
So great. How do you find the value of the above term? It is time consuming.
Let us look at another alternative.
What happens in compound interest?
Interest is paid on interest.
In the first year, interest is paid only on the principal. That is very similar to simple interest.
However, from the second year onwards things change. In the second year, you pay interest on the principal and also interest on interest.
Therefore, the Amount at the end of 2nd year in compound interest can be computed as follows
1 * Principal + 2* Simple interest on principal + 1 * interest on interest.
Similarly, if you were to find the Amount at the end of 3 years in compound interest use the following method
1*Principal + 3 * Simple interest on principal + 3 * interest on interest + 1 * interest on interest on interest
Let us see how it works in our example.
The principal is Rs.1500. The rate of interest is 20%. Therefore, the simple interest on principal is 20% of 1500 = Rs.300
The interest on interest = 20% interest on the interest of Rs.300 = 20% of Rs.300 = Rs.60.
Interest on interest on interest = 20% of Rs.60 = Rs.12.
Now add all these
Amount at the end of 3 years = 1*Principal + 3 * Simple interest on principal + 3 * interest on interest + 1 * interest on interest on interest
= 1500 + 3*300 + 3*60 + 1*12 = 1500 +900 + 1800 +12 = 2592.
You will get the same answer if you had used the formula. However, the calculation in this case was far easier than using the formula.
Try out the same method for four and five years and remember the 1-2-1, 1-3-3-1, 1-4-6-4-1 etc method which you can use comfortably in the exam.
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