Question

The difference between compound interest and simple interest on an amount of Rs.

10,000 for 2 years is Rs. 64. What is the rate of interest per annum ?​

Answer 1

Answer:

Step-by-step explanation:

Difference Between the Compound and Simple Interest

Sometimes you are given a situation and you have the option of repaying more it through compound interest or through simple interest. Obviously, you will choose simple interest because it is a cheaper option. Also, in compound interest, you are asked to pay the principal amount by levying interest on interest. But you would still need to determine the difference between the compound and simple interest. If the difference asked is for either two or three years than you can easily solve it through the formulas. Here are the formulas to the calculated difference in interests.

LET THE RATE OF INTEREST BE ‘x’ %

15000*[ (1+x/100)^2 -( 1+2*x/100 ] = 96

1 + 2*x/100 + x^2/10000 - 1 - 2*x/100 - 0.0064 = 0,; x^2 = 64

SOLVING ‘x’ = 8. ANSWER : RATE OF INTEREST = 8%

Answer 2

Step-by-step explanation:

Let the required ( R) rate of interest be r

(P) Principle = 10000

(T) Time=2 years

Difference between SI and CI = ₹64

Formula for SI = P×R×T /100

= 10000×2×r/100

= 200r

Formula for CI = P[(1+ R/100)^T-1]

= 10000[(1+r/100)^2-1

= 10000×(100+r/100)^2-10000

= 10000×(100+r)^2/10000-10000

= (100+r)^2-10000

According to the question

(100+r)^2-10000-200r =64

(100+r)^2-200r=10000+64

10000+(r^2)+200r -200r =10064

(r^2)=10064-10000

(r^2)=64

r = √64

r = 8% p.a.