Arif took a loan $R s . 80, 000$ from a bank at the rate of $10 %$ per annum. Find the difference in amounts he would be paying after $1 \frac{1}{2}$ years if the interest is compounded annually.

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Solution

For first year

$P = 80000, R = 10$ $, T = 1$

$I n t e r e s t = \frac{P R T}{100} = \frac{(80000 \times 10 \times 1)}{100} = 8000 A m o u n t = I n t e r e s t + P r i n c i p l e = 80000 + 8000 = 88000$

For second year principle will be amount of previous year (since interest is compounded)

$P = 88000, T = 6 m o n t h s = \frac{6}{12} y e a r s = 0.5, R = 10$
$I n t e r e s t = \frac{P R T}{100} = \frac{(80000 \times 10 \times 0.5)}{100} = 4400 T o t a l i n t e r e s t = 8000 + 4400 = 12400$
the difference he pays is the total interest which is $R s .12400 .$

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