Question

Find the difference between CI (compounded half-yearly) and SI on Rs. 10000 for 1.5 years at the rate of 20% per annum?

Answer 1

Given:

Find the difference between CI (compounded half-yearly) and SI on Rs. 10000 for 1.5 years at the rate of 20% per annum?

To find:

The difference

Solution:

The sum of money, P = Rs. 10000

The no. of years, n or T = 1.5 years

The rate of interest, R = 20%

Compound Interest (half-yearly):

n = 1.5 years = $(\frac{3}{2} \times 2) \:half-years = 3 \:half-years$

R = 20% p.a. = $\frac{20}{2} = 10\%\:half -years$

∴ $A = P [1 + \frac{\frac{R}{2} }{100} ]^2^n = 10000 [1 + \frac{10}{100} ]^3 = 10000[\frac{110}{100} ]^3 = 13310$

and

∴ $C.I._(_h_a_l_f_-_y_e_a_r_l_y_) = A - P = 13310 - 10000 =\bold{ 3310}$

Simple Interest:

$S.I. = \frac{P\:\times\: R\:\times\: T}{100} = \frac{10000\:\times\: 20\:\times\: 1.5}{100} = 100 \times 20 \times 1.5 = \bold{3000}$

Now,

The required difference is,

= $C.I._(_h_a_l_f_-_y_e_a_r_l_y_) - S.I.$

= $3310 - 3000$

= $\bold{310}$

Thus, the difference between CI (compounded half-yearly) and SI on Rs. 10000 for 1.5 years at the rate of 20% per annum is → Rs. 310.

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Answer 2

Given :- Find the difference between CI (compounded half-yearly) and SI on Rs. 10000 for 1.5 years at the rate of 20% per annum ?

Answer :-

when rate is compounded Half - Yearly :-

• We know that Half yearly Means Half of a year, when we Multiply it with 2 we will get a year . So we can say that in this case :-
• Rate is Divided by 2.
• Time is Multiply by 2 . ( To make it a complete year).

so,

• Rate = 20/2 = 10% per annum.
• Time = 1.5 * 2 = 3 years.

now, we know that,

• The difference between CI for 3 years = {P * (R)² * (300 + R)} / (100)³

putting values we get,

→ D = {10000 * (10)² * (300 + 10)} / (100)³

→ D = (10000 * 100 * 310) / 1000000

→ D = Rs.310 (Ans.)

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