Question

A sum of money lent out at C.I. at a certain rate per annum becomes three times of itself in 8 years. Find in how many years will the money become twenty-seven times of itself at the same rate of interest p.a.

a) 12 years
b) 16 years
c) 24 years
d) 32 years

Answer 1

Given that a sum of money triples over a period of 8 years, we use the property that 27 is 3 cubed to deduce that at the same compound interest rate, the money will become twenty-seven times of itself in 24 years.

Step-by-step explanation:

The question involves understanding the concept of compound interest and how it is applied to determine how long it will take for an investment to grow to a certain multiple of its original value. Given that a sum of money becomes three times of itself in 8 years, we want to find out when it will become twenty-seven times of itself.

Using the concept of compound interest, we can express this mathematically as:

1. The current scenario: Original Amount × (1 + Rate)^8 = 3 × Original Amount.
2. The future scenario: Original Amount × (1 + Rate)^n = 27 × Original Amount.

We know that 27 is 3 to the power of 3 (3³). Since the money triples every 8 years, we are looking for a time period that is 3 times that of 8 years to make the money grow to 3³ times its original amount. Thus, the money will become twenty-seven times of itself in 8 years × 3 = 24 years.