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A certain sum is lent at a certain rate of compound interest. It grows to 1.44 times its value in 2 years. If the same sum is lent at simple interest at the same rate, in how many years would it double itself?

Solution

✅ Correct Option: 3
  1. Let's say rate = r%

For compound interest in 2 years:

P(1+r100)2=1.44PP(1 + \frac{r}{100})^2 = 1.44P

(1+r100)2=1.44(1 + \frac{r}{100})^2 = 1.44

1+r100=1.21 + \frac{r}{100} = 1.2

r=20%r = 20\%

  1. Now for simple interest to double:

P(1+20t100)=2PP(1 + \frac{20t}{100}) = 2P

Where t is time in years

1+20t100=21 + \frac{20t}{100} = 2

20t100=1\frac{20t}{100} = 1

t=5t = 5

Therefore, at simple interest, the sum will double in 5 years.

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