If compounded quarterly on the sum of 15000 , difference between ci and si is 986 for 3 years ,then find rate of interest?
Answers
rate of interest would be 12 % per annum.
initial amount , P = 15,000 Rs.
time , n = 3 years = 3 × 12/3 = 12 quarters.
late rate of interest per annum is r.
then, rate of interest quarterly is r/4.
now compound interest, CI = P{(1 + r/400)ⁿ - 1}
= 15000[(1 + r/400)¹² - 1] .......(1)
simple interest, S.I = Prt/100
= 15000 × r × 3/100
= 450r .......(2)
now C.I - S.I = 986
⇒15000[(1 + r/400)¹² - 1 ] - 450r = 986
it's hard to solve direct method. we have to use binomial expansion.
(1 + r/400)¹² = 1 + 3r/100 + 33r²/80000 + .... ≈ 1 + 3r/100 + 33r²/80000
now, 15000 [(1 + 3r/100 + 33r²/80000) - 1] - 450r = 986
⇒15000 [3r/100 + 33r²/80000] - 450r = 986
⇒450r + 3 × 33r²/16 - 450r = 986
⇒99r²/16 = 986
⇒r² = 986 × 16/99 = 159.35
⇒r = 12.62 but we take r = 12 because we have not used many terms of binomial expansion. so more perfection we should take r = 12 %
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