Question

8. Find the Principal amount. If the difference of.S.I
and C.I at 12.5% per annum for 3 years is Rs. 750.
​

Answer 1

Given:

The difference between S.I. and C.I. = Rs. 750

The rate of interest = 12.5% p.a.

Time period = 3 years

To find:

The principal amount

Solution:

To solve the above-given problem we will use a direct formula of finding the difference between compound interest & simple interest for 3 years.

$\boxed{\boxed{\bold{Difference = PR^2 \bigg(\frac{R + 300}{(100)^3}\bigg) }}}$

where

P = principal amount

R = rate of interest

Now, substituting the values diff = 750, R = 12.5% in the formula, we get

$750 = P(12.5)^2 \bigg(\frac{12.5\: +\: 300}{(100)^3}\bigg) }}}$

$\implies 750 = P\times 156.25\times \bigg(\frac{312.5}{(100)^3}\bigg) }}}$

$\implies 750 = P\times \bigg(\frac{48828.125}{(100)^3}\bigg) }}}$

$\implies P = \frac{750\:\times\: (100)^3}{48828.125}$

$\implies P = \frac{750000000}{48828.125}$

$\implies \bold{P = Rs.\: 15360}$

Thus, the principal amount is Rs. 15360.

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