Vincen wrote:A sum of money is invested under compound interest for a few years. After how many years will the sum of money become nine times its present value?

(1) The sum of money invested under compound interest at the same rate of interest per annum became thrice its value in 6 years.
(2) The sum of money, under compound interest, at the same rate of interest per annum, would become twenty-seven times its present value in 9 years.

The OA is D.

The statement (2) alone is sufficient? Why?

We know that

A = P(1 + r/100)^n

Where A = Amount; P = Principal; r = rate of interest; and n = number of years

=> A/P = (1 + r/100)^n

We are given that A/P = 9, and we have to find out the value of n.

Thus, 9 = (1 + r/100)^n

If we get the value of r, we get the value of n.

Question rephrased: What's the value of r?

Statement 1: The sum of money invested under compound interest at the same rate of interest per annum became thrice its value in 6 years.

We have A/P = 3 and n = 6

Thus, 3 = (1 + r/100)^6

Thus, we can get the unique value of r. Sufficient.

There is no need to calculate the value if you are sure that you get the unique value.

For the sake of understanding, let's calculate it.

We have 3 = (1 + r/100)^6

Squaring both the sides, we get

(3)^2 = [(1 + r/100)^6]^2

9 = (1 + r/100)^12

=> The sum of money becomes nine times its present value in 12 years.

Statement 2: The sum of money invested under compound interest at the same rate of interest per annum became twenty-seven its value in 18 years.

I think there is a typo. Statements are not consistent. Either data in Statement I is wrong on that in II is wrong.

I assumed a typo in Statement 2. Instead of 9 years, it should be 18 years.

So, we have A/P = 27 and n = 18

Thus, 27 = (1 + r/100)^18

Thus, we can get the value of r. Sufficient.

Again, there is no need to calculate the value if you are sure that you get the unique value.

For the sake of understanding, lets' calculate it.

We have 27 = (1 + r/100)^18

(3)^3 = (1 + r/100)^18

Taking cube root of both the sides, we get,

3 = [(1 + r/100)^18]^1/3

3 = (1 + r/100)^6

Above is the same statement that we got in Statement 1. Sufficient.

The correct answer: D

Hope this helps!

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-Jay
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