In how many years does a sum of money becomes three times itself at 12.5 per annum simple interest

Answer

Hint:- In 8 years money from Interest will be come equal to the principal
amount invested. So, money had been doubled in 8 years.

Let the initial amount of money invested will be Rs. x.
Then after 8 years money had become 2x.
Out of Rs. 2x, money from interest will be 2x – initial amount invested = 2x – x = x.
Let the rate of interest be r.

So, now we will use a simple interest formula.
According to Simple Interest (S.I) formula.
\[ \Rightarrow S.I. = \dfrac{{PRT}}{{100}}\]. Where P is principal amount, R is rate of interest and T will be time period.

So, putting the values in the above formula. We will get,
\[ \Rightarrow x = \dfrac{{xr(8)}}{{100}}\]
On solving the above equation. We will get,
\[ \Rightarrow {\text{ }}r{\text{ }} = {\text{ }}\dfrac{{100}}{8}{\text{ }} = {\text{ }}12.5\]

Hence, the rate of interest to double a money in 8 years will be 12.5% per annum.

Note:- Whenever we came up with this type of problem where we are asked to
find rate of interest then first, we will find the interest on principal amount by
subtracting principal amount from the money after 8 years and then we will
assume rate of interest to be r and then apply, Simple Interest formula and
find the required value of rate of interest.

• Interests

A sum of money becomes 3 times in 5 years at simple interest. In how many years will the same sum become 6 times at the same rate of simple interest?

1. 10.5 years
2. 12 years
3. 12.5 years
4. 10 years

Answer

Let principal amount be ₹ P and rate of interest be R per annum. Time of investment is 5 years.

So, first we need to find R such that

P × (1+5R) = 3 × P

⇨ 1 + 5R = 3

⇨ R = 2/5 = 0.4 or 40%

Now, we need to find the number of years T such that,

P × (1 + 0.4T) = 6 × P

1 + 0.4T = 6

0.4T = 5

T = 5/0.4 = 25/2 = 12.5

The correct option is C.

Let, Principal amount be P.Rate of interest be R per annum. Time of investment is (T)=12 years.Sum of the money becomes three times in 12 years.⇒A=3P.⇒A=P+(P×T×R100)⇒3P=P(1+T×R100)⇒3=1+12×R100⇒3−1=12R100⇒2=3R25⇒50=3R⇒503=RNow, we need to find the number of years T such that, Sum of the money becomes five times.⇒5P=P(1+T×R100)⇒5=1+T×503×100⇒5−1=T×13×2⇒4=T6⇒24=Twill it become 5 times at the same rate of simple interest 24 years.

How many years does a sum of money becomes 3 times itself at 12.5% pa simple interest?

In what time a sum will become triple at 12.5% interest rate per annum?

At what time will a sum of money put at 12% simple interest triple itself?

In what time will a sum of money double itself at 12.5% per annum simple interest?