A Sum of Money Doubles Itself at a Compound Interest in 15 Years GMAT Problem Solving

Question: A sum of money doubles itself at a compound interest in 15 years. In how may years it will become 8 times?

1. 30 years
2. 40 years
3. 45 years
4. 50 years
5. 60 years

Correct Answer: C
Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

• A sum of money doubles itself at a compound interest in 15 years.

Find out:

• The number of years it will become 8 times

Let’s assume the sum of the money be x and compound interest be 2x.
As per the formula of mathematical rule,

Compound interest = Principal (1+ rate of interest/100)^Time

=> 2x = x(1 + R/100)^15
=> (1+R/100)^15 = 2 …… (i)

Let the number of years be m.
Therefore, x(1+R/100)^m = 8x
(1+R/100)^m = 2^3
(1+R/100)^m = [(1+R/100)^15]^3 ….. [from equation (i)]
(1+ R/100)^m = (1+R/100)^45

On comparing both powers, we get
m=45 years
The number of years it will become 8 times =45 years.

Approach Solution 2:

The problem statement informs that:

Given:

• A sum of money doubles itself at a compound interest in 15 years.

Find out:

• The number of years it will become 8 times

Let the initial amount be 100.
The amount will be doubled in every 15 years
The final amount is 800

So the amount of 100 will be double in 15 years
Therefore, we need to multiply 100 by 2, i.e 100 * 2 = 200

Again the amount of 200 will be double in the next 15 years
Therefore, we need to multiply 200 by 2, i.e 200 * 2 = 400

Again the amount of 400 will be double in another 15 years
Therefore, we need to multiply 400 by 2, i.e 400 * 2 = 800

Therefore, the total number of years = 15+15+15 = 45 years

Approach Solution 3:

The problem statement implies that:

Given:

• A sum of money doubles itself at a compound interest in 15 years.

Find out:

• The number of years it will become 8 times

Let the initial amount be 1.
The amount will be doubled in every 15 years
Hence, (1+r)^15 = 2 …. (i)
As per the question, the final amount will be 8 times of the initial amount.
Hence, the final amount will be 8 considering 1 as the initial amount.
By cubing both sides of equation 1, we get
[(1+r)^15]^3 = 2^3
Or, [(1+r)^45] = 8

Hence, the amount will get eight times in 45 years.

“A sum of money doubles itself at a compound interest in 15 years”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. The topic has been taken from the book “GMAT Prep Plus”. The candidates need to evaluate each data of the GMAT Problem Solving questions in order to solve numerical problems. GMAT Quant practice papers help the candidates to analyse several types of questions that will enhance their mathematical knowledge.

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