At what rate percent per annum simple interest will a sum of money triples itself in 25 years?

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

Answer

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.

Simple interest

Aptitude

1. At what rate percent per annum simple interest , will a sum of money triple itself in 25 year?

1. 1. 8%
   2. 5%
   3. 6%
   4. 12 %

Correct Option: A

Let principal amount = P
As amount =3P, T=25 yr
∴ SI=3P-P=2P
∴ Rate R = (100 x SI)/(P x T)
where, SI= Simple Interest T = Time
= (100 x 2P)/(P x 25)=8%

A sum of money triples itself at 8% per annum over a certain time. The time taken is

1. 20 years
2. 22 years
3. 25 years
4. 30 years

Answer (Detailed Solution Below)

Option 3 : 25 years

Free

Fill in the Blanks (Correct Tense)

10 Questions 15 Marks 10 Mins

Given :

A sum of money triples itself at 8% per annum over a certain time.

Concept used :

SI(simple interest) = (P × R × T)/100   (Where P, R and T are respectively principle, rate of interest and time period)

Amount = principle + interest

Calculations :

Let principle money is X, after T years, principle money will be 3X at the rate per annum = 8 %
We know that,
Final Amount = simple interest + principle 
⇒ 3X = SI + X

⇒ SI = 2X
⇒ 2X = (X × 8 × T)/100
⇒ 2 = 8T/100
⇒ T = 200/8 = 25
∴ The correct choice is option 3.

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