Question

if the differences between simple interest and compound interest for 2 years at 5%is $15,then sum is​

Answer 1

Let Sum(p)=$x

Time(t)=2 years

Rate(r)=5%

$si = \frac{p \times r \times t}{100} \\ \\ = \frac{x \times 5 \times 2}{100} \\ \\ = \frac{10x}{100} \\ \\ = \frac{x}{10}$

SI=$$\frac{x}{10}$

$ci \: amount = p(1 + \frac{r}{100} ) {}^{t} \\ \\ = x(1 + \frac{5}{100} ) {}^{2} \\ \\ = x( \frac{105}{100} ) {}^{2} \\ \\ x \times \frac{105}{100} \times \frac{105}{100} \\ \\ x \times \frac{21}{20} \times \frac{21}{20} \\ \\ = \frac{441x }{400}$

CI Amount=₹$\frac{441x}{400}$

CI=Amount-Sum

$= \frac{441x}{400} - x \\ \\ = \frac{41x}{400}$

CI=$$\frac{41x}{400}$

Difference=$5

MEANS

$ci - si = 5 \\ \\ \frac{41x}{400} - \frac{x}{10} = 5 \\ \\ = \frac{41x - 40x}{400} = 5 \\ \\ = \frac{x}{400} = 5 \\ \\ x = 400 \times 5 \\ \\ x = 2000$

=$2000

$\boxed{\mathbf{Sum\implies\ 2000}}$