Question

The difference between the simple interest on a certain sum at the rate of 10 per annum for 2 years and compound interest which is compounded every 6 months is rs 124.05 wha is the principal sum?

Answer 1

Compound Interest on P at 10% for 2 years when interest is compounded half-yearly

 

=P(1+R2100/)2T−P=P(1+120)4−P=P(2120)4−PP1+R21002T-P=P1+1204-P=P21204-P

 

Simple Interest on P at 10% for 2 years = PRT100=P×10×2100=P5PRT100=P×10×2100=P5

 

Given that difference between compound interest and simple interest = 124.05

P*(2120)4−P−P5=124.05P*21204-P-P5=124.05

 

=>P[(2120)4−1−15]=124.05P21204-1-15=124.05

P=8000

Answer: The difference between the simple interest on a certain sum at the rate of 10%per annum for 2 years and compound interest which is compounded every 6 months is Rs.124.05. So the principal sum is Rs 8000

Answer 2

Let P be the sum of the equation

Hence, if rate of interest is 10% and time is 2 years, then the compound interest will be

P [1 + (R/2)/100] ^2T – P

P [1 + (10/2)/100] ^2*2 – P

P [1 + 1/20] ^4 – P

P [21/20] ^4 – P

Simple interest = P*R*T/100 = P * 10 * 2 /100 = P/5

Now, calculate the difference among both = 124.05

P [21/20] ^4 – P/5 = 124.05

On solving the equation,

P = 124.05 * 160000/2481 = 8000