Inverse Problems on Compound Interest - Principal


 
 
Concept Explanation
 

Inverse Problems on Compound Interest - Finding Principal

In this section, we shall discuss how to compute Principal when compound interest , Amount , Rate and time period is given.

Illustration: The difference between the compound interest and simple interest on a certain sum of money at 10% per annum for 2 years is Rs 500. Find the sum when the interest is compounded annually.

Solution:  Let the sum be Rs 100.

Computation of compound interest :

We have, Principal = Rs 100, R = 10% per annum and n = 2

Amount =Rsleft [ 100times left ( 1+frac{10}{100} right )^{2} right ]

                  =Rsleft [ 100times left ( frac{100+10}{100} right )^{2} right ]

                  =Rsleft [ 100times left ( frac{110}{100} right )^{2} right ]

                 =Rsleft [ 100times left ( frac{11}{10} right )^{2} right ]

               =Rs;121

So, C.I=Rs;121-Rs;100

               = Rs 21

Computation of simple interest :

We have, Principal = Rs 100, R = 10% per annum and time = 2 years

therefore S.I.=Rsleft ( frac{100times 10times 2}{100} right )

  therefore S.I.=Rs;20

Now, difference in C.I. and S.I. = Rs(21 - 20) = Rs 1

Now,

If difference between C.I. and S.I. is Re 1, sum = Rs 100

If difference between C.I. and S.I. is Rs 500, Sum = Rs (100 X 500) = Rs 500000

Hence, Principal = 500000

Sample Questions
(More Questions for each concept available in Login)
Question : 1

The difference between the compound interest and simple interest on a certain sum of money at 5% per annum for 2 years is Rs 700. Find the sum when the interest is compounded annually.

Right Option : A
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Explanation
Question : 2

Find the principal, if the compound interest compounded annually at the rate of 10%  per annum for three years is Rs 331.

Right Option : A
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Explanation
Question : 3

Find the Principal, if the compound interest compounded annually at the rate of 15% per annum for three years is Rs 5208.

Right Option : C
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Explanation
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