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# A man lends Rs.12500 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. of the first year and the compound interest for the third year.

Last updated date: 20th Mar 2023
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Hint: We are going to solve the given problem by using the formula of compound interest.
Formula for compound interest is $A = P\left( {1 + \frac{R}{{100}}} \right)$
Where, A is the amount, P is the principal (initial) amount, R is the rate of interest in %.
In the first year P = 12500, R = 12%
$A = 12500\left( {1 + \frac{{12}}{{100}}} \right)$
$A = 12500\left( {\frac{{112}}{{100}}} \right) = 14000$
Then the interest for the first year = Rs.14000 – Rs.12500 = Rs.1500
In Second year,
P=Rs.14000
Given R=15%
$A = 14000\left( {1 + \frac{{15}}{{100}}} \right) = 16100$
In Third year,
P = 16100
Given R = 18%
$A = 16100\left( {\frac{{115}}{{100}}} \right) = 16100$
$A = 16100\left( {\frac{{118}}{{100}}} \right) = 18898$
Then the interest for the third year = Rs.18998 – Rs.16100 = Rs.2898
$\therefore$Difference of interest between third and first year = Rs.2898 – Rs.1500 = Rs.1398
Note: Compound interest is a method of calculating interest where the interest earned over time is added to the principal amount.