Question

The ratio of difference of s.I and

c.I for 2 years and 3 years is 8 25 . Find the rate of interest.

Answer 1

Answer:

Step-by-step explanation:

Let the principle amount be 1

Simple interest = principle × rate × time

Compound interest = Principle (1 + r)^n - Principle

Doing the substitution we have :

Simple interest = 2 × 1 × r = 2r

Compound interest = (1 + r) ^3 - 1

Now :

2r/{(1 + r) ^3 - 1} = 8.25

2r = 8.25{(1 + r)^3 - 1

Divide by 8.25

0.2424r = (1 + r) ^3 - 1

Raise both sides to 1/3

0.6235r^1/3 = 1 + r - 1

0.6235r^1/3 = r

Raise both sides to 3

0.2424r = r^3

Divide through by r :

r^2 = 0.2424

r = square root of 0.2424

r = 0.4923

= 49.23%