At what rate Percent of simple interest a sum would double itself after 20 years?

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Solution : Let Rs. P doubles in 5 years at the rate of simple interest `r%` per annum. <br>`therefore Pxx2 = P + (P xx rxx 5) /100` <br> `rArr P xx 2 = P ((100 + r xx5) /100)` <br> `rArr 2 = (100 + r xx5) /100` <br> `rArr r xx 5 = 200 – 100` <br> `therefore r = 100 /5 = 20%`

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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.

1. 20%
2. 17%
3. 22%
4. 15%

Answer (Detailed Solution Below)

Option 1 : 20%

Formula for Simple Interest -

\(SI = \frac{{P \times R \times T}}{{100}}\)

Where,

P = Principal

R = Rate of interest

T = Time period

Let the required rate of interest be X.

According to the question, SI must be equal to 2 × P in order to make the final sum two times the original principal amount after 5 year.

\(\therefore {\rm{P}} = {\rm{}}\frac{{{\rm{P}} \times {\rm{X}} \times 5}}{{100}}\)

⇒ X = 20%

∴ Required rate of interest is of 20%.

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Solution

The correct option is A 5%
Given, time = 20 years.
Let the sum invested be ₹ 100.
So, the Amount received after 20 years = ₹ 200.

We know that,
Principal + Interest = Amount.
Hence, Interest = Amount - Principal = ₹ (200-100) = ₹ 100.

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×20100
Hence, R = 5%.

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