On a certain sum, the compound interest in $2$ years amounts to $4, 240$ . If the rates of interest for successive years are $10 %$ and $15 %$ respectively, find the sum.

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Solution

Let, the sum or principal $= P$ .
Given, C.I. $= 4240$ , $n = 2$ years, $r_{1} = 10 %$ and $r_{2} = 15 %$ .
$∴ A = P (1 + \frac{r_{1}}{100})$ $(1 + \frac{r_{2}}{100})$

$\Rightarrow A = P (1 + \frac{10}{100})$ $(1 + \frac{15}{100})$

$\Rightarrow A = P (\frac{11}{10})$ $(\frac{23}{20})$

$\Rightarrow A = P (\frac{253}{200})$ .......(1)

Also, $C . I . = A - P$
$\Rightarrow 4240 = P (\frac{253}{200}) - P$
$\Rightarrow 4240 = P (\frac{53}{200})$
$\Rightarrow P = 16, 000$

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On a certain sum, the compound interest in 2 years amounts to 4,240. If the rates of interest for successive years are 10% and 15%respectively, find the sum.

Let, the sum or principal =P.Given, C.I. =4240, n=2 years, r1=10% and r2=15%.∴A=P(1+r1100)(1+r2100)⇒A=P(1+10100)(1+15100)⇒A=P(1110)(2320)⇒A=P(253200).......(1)Also, C.I.=A−P⇒4240=P(253200)−P⇒4240=P(53200)⇒P=16,000

On a certain sum, the compound interest in $2$ years amounts to $4, 240$ . If the rates of interest for successive years are $10 %$ and $15 %$ respectively, find the sum.