Question

What principal will amount to $Rs.15000$ at $10\% $ per annum in $5$ years?

Answer 1

Hint:
We can find the interest using the principal, rate of interest and period of interest. But here principal is unknown. So we can write interest in terms of principal. Since the amount is the sum of principal and interest, substituting the amount we get the principal.

Useful formula:
The interest for a principal $P$ deposited for a period of $n$ years with the rate of interest $r$ is given by ,
$I = \dfrac{{Pnr}}{{100}}$
The amount received after the period is the sum of the principal and the interest.
$A = P + I$

Complete step by step solution:
It is given that,
Amount, $A = 15000$
Rate of interest, $r = 10\% $
Number of years, $n = 5$
We know that the interest for a principal $P$ deposited for a period of $n$ years with the rate of interest $r$ is given by ,
$I = \dfrac{{Pnr}}{{100}}$
Substituting the values we get the interest, $I = \dfrac{{P \times 5 \times 10}}{{100}} = \dfrac{P}{2}$
Now the amount received after the period is the sum of the principal and the interest.
That is Amount, $A = P + I$
Substituting we get,
$A = P + \dfrac{P}{2} = \dfrac{{3P}}{2}$
It is given that the amount is $Rs.15000$.
Substituting we get
$\dfrac{{3P}}{2} = 15000$
Multiplying both sides by $2$ we get,
$3P = 15000 \times 2 = 30000$
Dividing by $3$ we get,
$P = \dfrac{{30000}}{3}$
$ \Rightarrow P = 10000$

Therefore the answer is $Rs.10000$.

Note:
This question can be solved in a bit easier way. We have interest, $I = \dfrac{{Pnr}}{{100}}$ and amount, $ A = P + I$
So substituting for $I$ we get,
Amount, $A = P + \dfrac{{Pnr}}{{100}}$
$ \Rightarrow A = P(1 + \dfrac{{nr}}{{100}})$
Substituting rate and number of years we get,
$A = P(1 + \dfrac{{5 \times 10}}{{100}})$
Simplifying we get,
$A = P(1 + \dfrac{1}{2}) = \dfrac{{3P}}{2}$
So we got the relation between principal and the amount. By substitution we get the answer.