At what rate percent per annum simple interest will a sum treble itself in 16 years

Question:

Sean M.

Algebra

7 months, 4 weeks ago

Video Answer:

Get the answer to your homework problem.

Try Numerade free for 7 days

We don’t have your requested question, but here is a suggested video that might help.

Related Question

An investment made at 16% compounded quarterly for years- Find the number of periods. Find the Interest rate per perlod (as percent),

Discussion

You must be signed in to discuss.

Video Transcript

We're investing at 16% per year. You compound four times a year, because we're compounding quarterly. You add interest to the account. You can't hand four quarters in one year, part A says. Every three months, there are at least four. Nine years will be nine times four, 36 quarters. Number of periods is 36. I want to work at an interest rate for a period or quarters. The annual rate is 16 and divided by four. That's how many years it's been. I do it four times a year every three months, and we get 4% every three months.

1. 24 years
2. 48 years
3. 36 years
4. 12 years

Nội dung chính Show

• Answer (Detailed Solution Below)
• The correct option is A 20 yearsLet the principal be P. As per the question, Amount = 2(Principal) = 2P SI = Amount - Principal = 2P - P = P By formula, R=SI×100P×T R=P×100P×10 =10 % So, the rate is 10% per annum. Now, the sum gets tripled. A = 3(Principal) = 3P SI = 3P - P = 2P T=SI×100P×R T=2P×100P×10 = 20 years
• At what rate will a sum of money double itself in 16 years?
• How long will it take a sum of money to treble itself at 16% pa simple interest?
• In what time will a sum of money put at 15 simple interest triple itself?
• At what rate percent per annum simple interest will a sum travel itself in 16 years?

Answer (Detailed Solution Below)

Option 2 : 48 years

Formula:

SI = P × ​\(R \over 100\) × T​​

Calculation:

P = P × \(R \over 100\) × 24

R = \(25 \over 6\)%

Now, 2P = P ×\(25 \over 600\)× T

          T = 48 years 

Ace your Interest preparations for Simple Interest with us and master Quantitative Aptitude for your exams. Learn today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

No worries! We‘ve got your back. Try BYJU‘S free classes today!

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Solution

The correct option is A 20 yearsLet the principal be P. As per the question, Amount = 2(Principal) = 2P SI = Amount - Principal = 2P - P = P By formula, R=SI×100P×T R=P×100P×10 =10 % So, the rate is 10% per annum. Now, the sum gets tripled. A = 3(Principal) = 3P SI = 3P - P = 2P T=SI×100P×R T=2P×100P×10 = 20 years

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

= P and T = 16 yrs. Rate = 100 x P/P*16% = 6 ¼ % p.a.

How long will it take a sum of money to treble itself at 16% pa simple interest?

A sum of money triple itself at 16% p.a. at simple interest in 12.5 years.

In what time will a sum of money put at 15 simple interest triple itself?

So the answer for your question is 13Y and 4 months.

At what rate percent per annum simple interest will a sum travel itself in 16 years?

⇒R=2P×100P×16=12.5%

Answer

Verified

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.

At what rate percent simple interest will a sum treble itself in 16 years?

At what rate will a sum will triple itself in 16 years?

At what rate percent per annum simple interest will a sum of money treble itself in 8 years?

At what rate percent simple interest will a sum of money double itself in 16 years?