If we fix time period and the rate of interest, simple interest

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 Multiple Choice QuestionsShort Answer Type

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41.

If we fix time period and the rate of interest, simple interest changes proportionally with principal. Would there be a similar relationship for compound interest? Why?


For simple interest,

                Simple interest = space space space space space space space space space space fraction numerator straight P space cross times straight r cross times straight t over denominator 100 end fraction

          space space space space space space space space space SI over straight P equals Prt over 100 plus straight P equals rt over 100


Since rate and time period are constant, then SI directly according to P.
Thus, the simple interest changes in direct proportion with the principal.
For compound interest.

                   Compound interest = space space space space space space space space space space space space space space space space space space space space space straight P open curly brackets open parentheses 1 plus straight r over 100 close parentheses to the power of straight t minus 1 close curly brackets

 

                space space space space space space space space space space space space space space space space space space space space space space CI over straight P equals fraction numerator straight P open curly brackets open parentheses 1 plus begin display style straight r over 100 end style close parentheses to the power of straight t minus 1 close curly brackets over denominator straight P end fraction equals open curly brackets open parentheses 1 plus straight r over 100 close parentheses to the power of straight t minus 1 close curly brackets


Since, rate and time period are constant, then
 
                    space space space space space space space space space space space space space space space space space space space space space open curly brackets open parentheses 1 plus straight r over 100 close parentheses to the power of straight t minus 1 close curly brackets is constant.

i.e. CI changes with P
Thus, the compound interest also changes directly in proportion with principal.

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