Question

the difference between the compound interest and simple interest on a certain sum of money is 8% p.a. compounded annually for 3 yearsis Rs 308.the sum is​

Answer 1

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The difference between the compound interest and simple interest on a certain sum of money is 8% p.a. compounded annually for 3 yearsis Rs 308.the sum is?

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let ,the sum is =p Rs

given

rate of interest (r)is =8%

time(t)=3years

now for compound interest ,

$C_i= p((1 + \frac{r}{100} ) {}^{t} - 1 ) \\ putting \: the \: values \: \\ \implies C_i= p((1 + \frac{8}{100} ) {}^{3} - 1) \\ \implies C_i=p(( \frac{108}{100} ) {}^{3} - 1)$

now for simple interest ,

$S_i = \frac{prt}{100} \\ \implies S_i = \frac{p \times 8 \times 3}{100} = \frac{24p}{100}$

now....

according to the Question

$C_i-S_i=308 \\ \implies C_i-S_i=p(( \frac{108}{100} ) {}^{3} - 1) - \frac{24p}{100} \\ \implies 308=p[( \frac{108}{100} ) {}^{3} - 1 - \frac{24}{100} ] \\ \implies 308 = p[ \frac{108 {}^{3} - 100 {}^{3} - 24 \times 100 {}^{2} }{100 {}^{3} } ] \\ \implies 308 = p[ \frac{19712}{1000000} ] \\ \implies p = 308 \times \frac{1000000}{19712} \: \\ \implies p = 15625 \\ \therefore \: the \: sum \: was \: 15625 \: rs.$

$\large\mathfrak{...hope\: this \:helps\: you.....}$