Question

Find the rate of simple interest when the money doubles itself in 12 ½ years
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Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

↝ Sum of money invested be Rs p

So,

↝ Amount = Rs 2p

↝ Time Period, n = 12.5 years

Let rate of interest be r % per annum.

We know,

↝ Simple interest = Amount - Principal

So,

↝ Simple interest = 2p - p = p

Thus, we have

Principal = Rs p

Simple interest = Rs p

Time = 12.5 years

Rate = r % per annum

We know that,

Simple interest SI, on a certain sum of money of Rs p invested at the rate of r % per annum for n years is

$\rm :\longmapsto\:\boxed{ \tt{ \: SI = \frac{p \times r \times n}{100} \: }}$

So, on substituting the values, we get

$\rm :\longmapsto\:p = \dfrac{p \times r \times 12.5}{100}$

$\rm :\longmapsto\:1 = \dfrac{ r \times 125}{1000}$

$\rm :\longmapsto\:1 = \dfrac{ r}{8}$

$\rm \implies\:\boxed{ \tt{ \: r \: = \: 8 \: \% \: per \: annum \: }}$

More to know :-

Amount on a certain sum of money of Rs p invested at the rate of r % per annum compounded annually for n years is

$\rm :\longmapsto\:\boxed{ \tt{ \: Amount = {p\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \: }}$

Amount on a certain sum of money of Rs p invested at the rate of r % per annum compounded semi - annually for n years is

$\rm :\longmapsto\:\boxed{ \tt{ \: Amount = {p\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} \: }}$

Amount on a certain sum of money of Rs p invested at the rate of r % per annum compounded quarterly for n years is

$\rm :\longmapsto\:\boxed{ \tt{ \: Amount = {p\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} \: }}$

Answer 2

Step-by-step explanation:

p = p*r*12.5/100

r = 8% per annum