Interest - Quant/Math - CAT 2009

If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to treble if invested at the same rate of interest in a scheme where interest is computed using simple interest method?

(1)

9 years

(2)

22 years

(3)

18 years

(4)

33 years

Solution:

The sum of money grows to times in 2 years.
If P is the principal invested, then it has grown to P in two years when invested in compound interest.

In compound interest, if a sum is invested for two years, the amount is found using the following formula
= P in this case.
=> => => =>

If r = , then in simple interest the time it will take for a sum of money to treble is found out as follows:

Let P be the principal invested. Therefore, if the principal trebles = 3P, the remaining 2P has come on account of simple interest.

Simple Interest = , where P is the simple interest, r is the rate of interest and ‘n’ is the number of years the principal was invested.

Therefore, 2P = => 2 = or n = 22 years.

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