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A sum of money is invested at a compound interest for 9 months at 20 percent per annum compounded semi annually. If the interest were compounded quarterly, it would have fetched rs 210 more than in the previous case. Find the sum
Asked by GJain7394 | 20 Sep, 2022, 02:44: PM
answered-by-expert Expert Answer
When the interest is compounded half-yearly, we have
Amount equals straight P open parentheses 1 plus fraction numerator straight r over denominator 2 cross times 100 end fraction close parentheses to the power of 2 cross times straight n end exponent equals straight P open parentheses 1 plus 20 over 200 close parentheses to the power of 2 cross times 3 over 4 end exponent equals straight P open parentheses 11 over 10 close parentheses to the power of 3 over 2 end exponent space space space space........ space left parenthesis straight I right parenthesis When space the space interest space is space compounded space quarterly comma space we space have Amount equals straight P open parentheses 1 plus fraction numerator straight r over denominator 4 cross times 100 end fraction close parentheses to the power of 4 cross times straight n end exponent equals straight P open parentheses 1 plus 20 over 400 close parentheses to the power of 4 cross times 3 over 4 end exponent equals straight P open parentheses 21 over 20 close parentheses squared space space space space........ space left parenthesis II right parenthesis As space per space the space question comma space we space have straight P open parentheses 21 over 20 close parentheses squared minus straight P open parentheses 11 over 10 close parentheses to the power of 3 over 2 end exponent equals 210 rightwards double arrow straight P open square brackets open parentheses 21 over 20 close parentheses squared minus open parentheses 11 over 10 close parentheses to the power of 3 over 2 end exponent close square brackets equals 210 rightwards double arrow straight P equals fraction numerator 210 over denominator open square brackets open parentheses 21 over 20 close parentheses squared minus open parentheses 11 over 10 close parentheses to the power of 3 over 2 end exponent close square brackets end fraction space almost equal to space Rs.53364
Answered by Renu Varma | 06 Oct, 2022, 12:00: PM

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