A man lends Rs. $12, 500$ at $12$ % for the first year, at $15$ % for the second year and at $18$ % for the third year. If the rates of interest are compounded yearly; find the difference between the C.I. for the first year and the compound interest for the third year.

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Solution

For the first year, on interest being compounded at $R = 12$ %, we have
$A m o u n t = P {(1 + \frac{R}{100})}^{N} = 12, 500 \times {(1 + \frac{12}{100})}^{1} = 12, 500 \times 1.12 = R s 14, 000$
For the second year, $P = R s 14, 000$ on interest being compounded at $R = 15$ %, we have
$A m o u n t = P {(1 + \frac{R}{100})}^{N} = R s 14, 000 \times {(1 + \frac{15}{100})}^{1} = R s 14, 000 \times 1.15 = R s 16, 100$

For the third year, $P = R s 16, 100$ on interest being compounded at $R = 18$ %, we have
$A m o u n t = P {(1 + \frac{R}{100})}^{N} = R s 16, 100 \times {(1 + \frac{18}{100})}^{1} = R s 16, 100 \times 1.18 = R s 18, 998$

Now, $C . I .$ for the first year $= A - P = 14, 000 - R s 12, 500 = R s 1, 500$

And, $C . I .$ for the third year $= A - P = 18, 998 - R s 16, 100 = R s 2, 898$

Required difference between the C.I. for the first year and third year $= R s 2, 892 - R s 1, 500 = R s . 1, 398$

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A man lends Rs. 12,500 at 12% for the first year, at 15% for the second year and at 18% for the third year. If the rates of interest are compounded yearly; find the difference between the C.I. for the first year and the compound interest for the third year.

A man lends Rs. $12, 500$ at $12$ % for the first year, at $15$ % for the second year and at $18$ % for the third year. If the rates of interest are compounded yearly; find the difference between the C.I. for the first year and the compound interest for the third year.