Inverse Problems on Compound Interest Time Period


 
 
Concept Explanation
 

Inverse Problems on Compound Interest - Finding Time Period

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

Illustration: In what time Rs 800 amount to rs 882 at 5% per annum compounded annualy?

Solution: We have, P = Principal = Rs 800, A = amount = Rs 882 and Rate R = 5% per annum

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

882 =800 left ( 1+frac{5}{100} right )^{n}

frac{882}{800}=left ( 1+frac{1}{20} right )^{n}

frac{882}{800}=left ( frac{20+1}{20} right )^{n}

frac{882}{800}=left ( frac{21}{20} right )^{n}

frac{441}{400}=left ( frac{21}{20} right )^{2}

frac{21^{2}}{20^{2}}=left ( frac{21}{20} right )^{n}

left (frac{21}{20} right )^{2}=left ( frac{21}{20} right )^{n}

As the base is same. So, by comparing the powers, we have

n = 2

Hence, required time is 2 years.

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

In how much time will a sum of Rs 1600 amount to Rs 1102.50 in 2 years at compound interest?

Right Option : A
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Explanation
Question : 2

The compound interest on Rs 1600 at 10% per annum for a certain period of time is Rs 336. Find the time in years.

Right Option : D
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Explanation
Question : 3

The compound interest on Rs 1800 at 10% per annum for a certain period of time is Rs 378. Find the time in years.

Right Option : D
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Explanation
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