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Question

A sum of money, invested at compound interest, amounts to Rs. $$19,360$$ in $$2$$ years and to Rs. $$23,425.60$$ in $$4$$ years. Find the original sum of money.


Solution


On interest being compounded for $$2$$ years, $$ Amount = P{(1 + \frac {R}{100})}^{N} $$
$$ \implies 19,360 =  P{(1 + \frac {R}{100})}^{2} $$  --- (1)
On interest being compounded for $$4$$ years, $$ Amount = P{(1 + \frac {R}{100})}^{N} $$
$$ \implies 23,425.60 =  P{(1 + \frac {R}{100})}^{4} $$  --- (2)
Dividing, eqn (2) by eqn (1)
$$ 1.21 = {(1 + \frac {R}{100})}^{2} $$
Taking square root on both sides,
$$ 1.1 = 1 + \frac {R}{100} $$
$$ \implies 0.1 = \frac {R}{100} $$
$$ \implies R = 10 $$ %
Putting the value of $$R$$ in eqn $$(1),$$ we get
$$ \implies 19,360 =  P{(1 + \frac {10}{100})}^{2} $$
$$ \implies19,360 =  P \times {(1.1})^{2} $$
$$ \implies P = \frac {19,360}{1.21} $$
$$ \implies P = Rs.  16,000 $$

Mathematics

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