Question

if the difference between ci and si for 1.5 years at 22 2/9 % p a compounded half yearly is 5600, find difference between ci and si for 1 years at same rate (compounded half yearly

Answer 1

Answer:

Let the principal = x

now a/q ,

CI =

$x \times (1 + \frac{200}{9 \times 200} ) {}^{3} - x = x \times ( \frac{10}{9} ) {}^{3} - x = x( \frac{1000}{729} - 1) = \frac{271}{729} x$

& SI =

$\frac{x \times 200 \times 3}{9 \times 200} = \frac{x}{3}$

CI - SI = 5600

i.e

$\frac{271}{729} x - \frac{x}{3} = x( \frac{271 - 243}{729} ) = \frac{28}{729} x = 5600$

$28x = 5600 \times 729$

$x = \frac{5600 \times 729}{28} = 145800$

now for one year, Required Difference =

$145800 \times (1 + \frac{200}{9 \times 200} ) {}^{2} - 145800 - \frac{145800 \times 200 \times 2}{9 \times 200} = 145800 \times ( \frac{100}{81} - 1) - 32400 = 145800 \times \frac{19}{81} - 32400 = 34200 - 32400 = 1800 \: \: ans.$