Question

The difference between simple interest and compound interest on a certain principal for 2 years at 4% is Rs. 36. Find the principal.​

Answer 1

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We first find the simple interest and compound interest assuming the principal to be Rs. x. Then, find the difference between S.I. and C.I. Taking this difference for Rs. x we can find the principal.

$let \: the \: prinecipal \: P = rs.x , \: R = 4\% \: and \: N = 2yrs$

$simple \: interest$

$I = \frac{P \times N \times R}{100} = \frac{x \times 2 \times 4}{100} = rs.\frac{8x}{100}$

$now \: compound \: interest \: is$

$A = P(1 + \frac{R}{100} {)}^{n} = n(1 + \frac{4}{100} {)}^{2} = x(1.04 {)}^{2} = (1.0816)x \: rs.$

$Hence \: compound \: interest = 1.0816x - x = 0.0816x$

$Now, \: C.I.-S.I. = 0.0816x - \frac{8x}{100} = \frac{8.16x - 8x}{100} = \frac{0.16x}{100}$

The difference in CI and SI is Rs. 0.16 when the principal is Rs. x.

But the difference is Rs. 36 then the principal

$is \: x = \frac{100}{0.16} \times 36 = 22,500.$

$thus \: the \: principal \: is$

$\boxed{rs.22,500}$