Question

A sum of 10,000 yields 3310 as compounded internet in 3 years.If year is compounded yearly, find the amount and rate of interest.​

Answer 1

hope it is correct friends

Answer 2

The amount is $13,310 rs$ and rate of interest is $10\%$

Step-by-step explanation:

Given values are

Sum $= 10,000 rs$

Compound interest  (C.I)  $= 3310rs$

Time (T)  $= 3 year$

Rate of interest (R) = $R \%$

Amount = A

We have to find out the rate of interest and amount

The rate of interest is given by below formula

Compound interest is given by

                             C.I $= Sum \times ( 1 + \frac{R}{100} )^T - Sum$

                             C.I $= Sum \{ (1 + \frac{R}{100} )^T - 1 \}$

                          $3310 = 10,000 \{ (1+ \frac{R}{100}) ^3- 1 \}$

                          $\frac{3310}{10000} = (1+ \frac{R}{100} )^3 - 1$

                          $\frac{331}{1000} + 1 = (1+ \frac{R}{100} )^3$

                                $\frac{1331}{1000} = (1+ \frac{R}{100} )^3$

                              $(\frac{11}{10} )^3 = (1+ \frac{R}{100} )^3$

                                      $\frac{11}{10} = 1+ \frac{R}{100}$

                                      $\frac{R}{100} = \frac{11}{10} - 1$

                                       $\frac{R}{100} = \frac{1}{10}$

                                       $R = 10\%$

So, Rate of interest is $\%10$

     Now we have to find out amount

     for amount below formula is used

                 $Amount = Sum + C.I$

                 $Amount = 10,000 + 3310\\amount = 13,310 rs$

         Thus, Rate of interest $= 10\%$

                   Amount $=13310 rs$