In what time a sum of money will triple itself at a rate of simple interest of 4% per annum?

Let the sum of money be x

Amount = 3 × Rs x

= Rs 3x

Interest = Amount – Principal

= Rs 3x – Rs x

= Rs 2x

Rate =13 \frac{1}{3} \% \text { p.a. }

= 40 / 3 % p.a.

Time (T) = (I × 100) / (P × R)

= (2x × 100) / x × (40 / 3) years

On further calculation, we get,

= (2 × 100 × 3) / 40 years

= (100 × 3) / 20 years

We get,

= 5 × 3 years

= 15 years

A. 5 yrs

B. 10yrs

C. 15 yrs

D. 20 yrs

A sum invested on simple interest becomes triple itself in 16 years. Then the rate of interest is?

Answer

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Hint: We will assume the sum invested as x rupees. We have been given that it becomes triple after 3 years which means it becomes 3 x. Now, we know that the final amount = principal amount + simple interest. So, we will find the simple interest from that and using the formula, $\text{simple interest}=\dfrac{\text{principal amount}\times \text{time}\times \text{rate}}{100}$, we will find the rate of interest.

Complete step-by-step answer:
We are given the time period as 16 years and that the sum becomes triple after 16 years. So, we will first assume the sum invested as Rs. x. We have been given that after 16 years, it becomes triple, so,
Final amount = $3\times x=3x$.
Now, we know that the final amount is the summation of the principal amount and simple interest,
Final amount = principal amount + simple interest, which can be written as,
3 x = x + simple interest, so we get the simple interest as = 3 x - x = 2 x.
Now, we have the principal amount, time and the simple interest, so we will find the rate using the formula, $\text{simple interest}=\dfrac{\text{principal amount}\times \text{time}\times \text{rate}}{100}$. So, by substituting the values of the parameters we get,
$\begin{align}
  & \dfrac{2x}{1}=\dfrac{x\times 16\times rate}{100} \\
 & \Rightarrow \dfrac{2}{1}=\dfrac{16\times rate}{100} \\
\end{align}$
On cross-multiplying, we get,
$\begin{align}
  & rate=\dfrac{2\times 100}{16} \\
 & \Rightarrow rate=12.5\% \\
\end{align}$
Hence, we get the rate of interest as 12.5 %.

Note: There is a possibility that the students think that the simple interest becomes triple of the principal amount, that is simple interest is 3 x. So, in further calculations for finding the rate of interest, they will end up with, $rate=\dfrac{3\times 100}{16}\Rightarrow 18.75\%$. But students should read the question carefully to understand that the sum becomes triple, which means the principal amount becomes triple after 16 years.

Solution

Let the principal ( P ) = Rs x

Amount = A = Rs 3x

Simple interest ( I ) = A - P

I = 3x - x

I = 2x

Rate of interest ( R ) = 40/3 %

Let time = T years

PTR/ 100 = I

T = ( 100 I ) / PR

= ( 100 × 2x ) / ( x × 40/3 )

= ( 100 × 2 × 3 ) / 40

= 15

Therefore ,

T = 15 years

I hope this helps you.

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Important Civilization in Rajasthan

15 Questions 15 Marks 10 Mins

Given:

Rate (R) = 20%

Formula used:

S.I. = (P × R × T)/100

Where, S.I. → Simple Interest

P → Principal

R → Rate 

T → Time 

Calculations:

Let the sum of money be  Rs. P.

So, A = 3P

And S.I. = A - P = 3P – P = 2P

Thus T = (100 × S.I.)/(P × R) 

⇒ T = (100 × 2P)/(P × 20) = 10 years

∴ The required time is 10 years.

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