Kamal and Anand each lent the same sum of money for $2$ years at $5$ % at simple interest and compound interest respectively. Anand received Rs. $15$ more than Kamal. Find the amount of interest received by Anand.

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Solution

For Kamal,
$N = 2 y e a r s$
$R = 5$ %

We have $S . I . = \frac{P N R}{100} = \frac{P \times 2 \times 5}{100} = \frac{10 P}{100} = 0.1 P$

And for Anand, on interest being compounded for $2$ years and $R = 5$ %, $A m o u n t = P {(1 + \frac{R}{100})}^{N} = P {(1 + \frac{5}{100})}^{2} = P \times ({1.05}^{2}) = 1.1025 P$

So, $C . I . = A - P = 1.1025 P - P = 0.1025 P$

Given, $C . I - S . I . = R s 15$
$=> 0.1025 P - 0.1 P = R s 15228$
$=> 0.0025 P = R s 15$
$=> P = R s 6, 000$

S.I. received for Kamal $= 0.1 P = 0.1 \times 6000 = R s 600$
And C.I. received for Anand $= 0.1025 P = 0.1025 \times 6000 = R s 615$

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Kamal and Anand each lent the same sum of money for 2 years at 5% at simple interest and compound interest respectively. Anand received Rs. 15 more than Kamal. Find the amount of interest received by Anand.

Kamal and Anand each lent the same sum of money for $2$ years at $5$ % at simple interest and compound interest respectively. Anand received Rs. $15$ more than Kamal. Find the amount of interest received by Anand.