Inverse Problems on Compound Interest - Rate


 
 
Concept Explanation
 

Inverse Problems on Compound Interest - Finding Rate

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

Illustration: At what rate percent per annum, compound interest will Rs 10000 amount to Rs 13310 in three years?

Solution:  Let the rate be R% per anum.

We have, P = Principal = Rs 10000, A = amount = Rs 13310 and n = 3 years

A=Pleft ( 1+frac{R}{100} right )^{n}

13310 =10000 left ( 1+frac{R}{100} right )^{3}

frac{13310}{10000}=left ( 1+frac{R}{100} right )^{3}

frac{1331}{1000}=left ( 1+frac{R}{100} right )^{3}

frac{11^{3}}{10^{3}}=left ( 1+frac{R}{100} right )^{3}

left ( 1+frac{R}{100} right )^{3}=left ( frac{11}{10} right )^{3}

  Taking cube root on both sides, we have

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

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

frac{R}{100} = frac{11-10}{10}

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

R = frac{100}{10}

R = 10

Hence, rate = 10% per annum.

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

 Find the rate percent per annum if Rs 2000 amount to Rs 2662 in 1frac{1}{2} years, interest being compounded half-yearly?

Right Option : D
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Explanation
Question : 2

At what rate percent will a sum of Rs 1000 amount to Rs 1102.50 in 2 years at compound interest?

Right Option : D
View Explanation
Explanation
Question : 3

At what rate percent compound interest per annum will Rs 640 amount to Rs 774.40 in 2 years?

Right Option : C
View Explanation
Explanation
 
 
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