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

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Solution

The correct option is A 50%Given, time = 2 years. Let the sum invested be ₹ 100. So, the Amount received after two years = ₹ 200. We know that, Principal + Interest = Amount. Hence, Interest = Amount - Principal = ₹ (200-100) = ₹ 100. (adsbygoogle = window.adsbygoogle || []).push({}); The Simple Interest earned on a sum of ₹ P for a period of T years at the rate of R% p.a S.I is given by P×R× T100. So, ₹ 100 = 100× R×2100 Hence, R = 50%.

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.

Free

Navik Section I: Official Model paper

60 Questions 60 Marks 45 Mins

Let the Principal be 100.

P = 100,  then A = 200 and SI will be 200 - 100 = 100 

SI = 100 for 10 years 

Rate = 100/10 = 10%.

∴ The rate of interest is 10%.

Traditional method:

Given: 

Time period = 10 years

Formula used:

SI = (P × R × T)/100

A = P + SI

Where, P = principal, R = rate, T = time, SI = simple interest

Calculations:

The sum of money is 2P

SI = 2P - P

⇒ P = (P × R × 10)/100

⇒ 1 = R/10

⇒ R = 10%

∴ The rate of interest is 10%.

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