Question

At what rate per cent per annum will Rs 3000 amount to Rs 3993 in 3 years,the interest being compounded annually?

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Answer 1

Answer:

here is your answer..... hope you understood...

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Answer 2

GIVEN :-

• principal ( p ) = rs 3000

• amount ( a ) = rs 3993

• time ( t ) or ( n )= 3 years

TO FIND :-

• rate of the compound interest ( r )

SOLUTION :-

NOW , we know that interest is being compound

so formula for compound interest :-

$\implies \boxed{ \rm{a = p(1 + \dfrac{r}{100} ) {}^{n} }}$

where ,

a = amount

p = principal

r = rate

n = time ( in years )

now put the values in formula

$\implies \rm{3993 = 3000(1 + \dfrac{r}{100} ) {}^{3} }$

$\implies \rm{(1 + \dfrac{r}{100} ) {}^{3} = \dfrac{3993}{3000} }$

$\implies \rm{(1 + \dfrac{r}{100} ) {}^{3} = \dfrac{1331}{1000} }$

$\implies \rm{ \sqrt[3]{ (1 + \dfrac{r}{100} ) {}^{3}} = \sqrt[3]{\dfrac{3993}{3000} } }$

$\implies \rm{ (1 + \dfrac{r}{100} ) = \dfrac{11}{10}}$

$\implies \rm{ \dfrac{r}{100} = \dfrac{11}{10} - 1}$

$\implies \rm{ \dfrac{r}{100} = \dfrac{11 - 10}{10} }$

$\implies \rm{ \dfrac{r}{100} = \dfrac{1}{10} }$

$\implies \rm{ r= \dfrac{100}{10} }$

$\implies \rm{ r = 10}$

$\implies \boxed{ \boxed{\rm{ rate \: = 10\% }}}$

OTHER INFORMATION :-

Compound Interest Definition :

• Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from the simple interest where interest is not added to the principal while calculating the interest during the next period.

• Compound interest finds its usage in most of the transactions in the banking and finance sectors and also in other areas as well.

• Some of its applications are:

• Increase or decrease in population The growth of bacteria.

• Rise or Depreciation in the value of an item.