How many years does a sum of money becomes three times itself at 12.5% per annum simple interest?

A sum of money, lent out at simple interest, doubles itself in 8 years. Find :
(i) the rate of interest
(ii) in how many years will the sum become triple (three times) of itself at the same rate percent?

Solution

Let P = Rs.100, A = Rs.200

I = Rs.200 − Rs.100 = Rs.100, T = 8 years

R =`(100xx"I")/("P"xx"T")=(100xx100)/(100xx8)`

`=100/8=25/2%`

Now again P = Rs.100

A = Rs.300

I = Rs.300 − Rs.100 = Rs.200

R = `25/2%`

T =`(100xx"I")/("P"xx"R")=(100xx200)/(100xx25/2)=(100xx200xx2)/(100xx25)`

= 16 Years

So the given sum of money will become triple in 16 years.

Concept: Concept of Principal, Interest, Amount, and Simple Interest

  Is there an error in this question or solution?

APPEARS IN

Answer

Verified

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.

Solution

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 (adsbygoogle = window.adsbygoogle || []).push({}); ⇒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?

How long will it take a certain sum of money doubles itself at 12.5% per annum simple interest?

In what time will a sum of money becomes three times?

What will be the rate of interest so that a sum amounts to its three times in 25 years?