# The difference between simple interest and compound interest on a cert

A. Rs. 5765.50

B. Rs. 5525.325

C. Rs. 5265.625

D. Rs. 6120.25

### Right Answer is: C

#### SOLUTION

Let the sum = P

The cumulative rate of interest for 3 years at SI = 20 +20 + 20 = 60%

In C.I.-

20% = 2/10

Means, 10 Rs. becomes 12 in one year.

In three years,

YEAR Principle Amount

1 yr 10 12

2 yr 10^{2} 12^{2}

3 yr 10^{3} 12^{3}Means, in 3 years, Rs. 1000 becomes Rs. 1728.

So, the cumulative rate of interest for three years =

=[(1728-1000)/1000]×100 = 72.8%

The Difference in Cumulative Rate of interest of S.I. and C.I. after 3 years = 72.8 – 60 = 12.8%

Difference in interest = = 674

P = Rs. 5265.625

**Alternating Method:**

If values are increased by a% and b% successively, then net increment = a + b + (axb)/100

Thus, effective rate of interest for 3 years at CI = 20 +20 + (20 x 20)/100 + 20 + [20 x (20 +20 + (20 x 20)/100 ]/100 = 72.8%

Difference in interest = = 674

P = Rs. 5265.625

The difference between simple interest and compound interest on a cert