At what rate percent per annum will a sum of money double itself in 16 years?

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Answer (Detailed Solution Below)
The correct option is A 5%Given, time = 20 years. Let the sum invested be ₹ 100. So, the Amount received after 20 years = ₹ 200. We know that, Principal + Interest = Amount. Hence, Interest = Amount - Principal = ₹ (200-100) = ₹ 100. The Simple Interest earned on a sum of ₹ P for a period of T years at the rate of R% p.a S.I is given by P×R× T100. So, ₹ 100 = 100× R×20100 Hence, R = 5%.
At what rate percent per annum will a sum double itself in 16 years?
At what rate of simple interest per annum will a sum triple itself in 16 years?
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Answer (Detailed Solution Below)

Option 1 : 20%

Formula for Simple Interest -

$SI = \frac{{P \times R \times T}}{{100}}$

Where,

P = Principal

R = Rate of interest

T = Time period

Let the required rate of interest be X.

According to the question, SI must be equal to 2 × P in order to make the final sum two times the original principal amount after 5 year.

$\therefore {\rm{P}} = {\rm{}}\frac{{{\rm{P}} \times {\rm{X}} \times 5}}{{100}}$

⇒ X = 20%

∴ Required rate of interest is of 20%.

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Last updated date: 27th Dec 2022

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Hint: - Here we go through by the formula of simple interest that we study in the chapter of simple interest. i.e.$SI = \dfrac{{P \times R \times T}}{{100}}$ . By this formula we will be able to calculate the rate.

Complete step-by-step answer:

Here in the question the principal amount is not given.
So let the principle amount be Rs x.
And according to the question at the end the amount become double that means
Amount=2x.
As we know the simple interest means principle amount subtracted from final amount i.e.
S.I= Amount-Principal amount
S.I=2x-x=x
Here the give time T=1o years
Now put these values in the formula of S.I i.e. $SI = \dfrac{{P \times R \times T}}{{100}}$ We get,
$
   \Rightarrow x = \dfrac{{x \times R \times 10}}{{100}} \\
   \Rightarrow R = \dfrac{1}{{10}} \times 100 \\
  \therefore R = 10\% \\
$
Hence the required rate in which the sum becomes double itself in 10 years is 10%.

Note: - Whenever we face such a type of question, the key concept for solving the question is to first assume the principal amount because the principal amount is not given and then proceed with the question to find the S.I. Then by putting the formula of S.I we will get the terms which we need to find.