Question

At what rate of percent compound interest does a sum of money become four times itself in 2 years​

Answer 1

Answer:

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1. We know A= P(1+x)ⁿ.
2. Where A= Amount= 4P
3. P= Principal
4. x= rate of interest = ?

• n= Number of years of deposit= 2.
• So 4P=P(1+x)²
• So (1+x)²= 4P/P= 4
• So (1+x)= √4= 2
• Therefore x = 1.
• That is the rate of interest= 100% !! .OK

Explanation:

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Answer 2

Explanation:

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100%

4x=x(1+100r)2

∵(1+100r)2=4 or 1+100r=2

or r=100%

At 100% rate of interest, the Principal doubles itself in one year. Since it is compound interest, the Principal for the second year would be 2P. This again doubles itself in another year because Interest rate is 100%.

So at the end of two years it becomes 4 P.

Hence at an interest rate of 100% , the sum of money becomes 4 times itself.