Question

The simple interest and compound interest of a sum of money in 3 years are Rs. 3300 and Rs. 3676.31 respectively. Find the annual rate of interest and the principal.​

Answer 1

Let P be the principal, r be the annual rate of interest, and n be the number of years.

Using the formula for simple interest, we have:

SI = P * r * n
3300 = P * r * 3

Using the formula for compound interest, we have:

CI = P * (1 + r/n)^(n * t)
3676.31 = P * (1 + r/1)^(1 * 3)

Simplifying the second equation, we get:

3676.31 = P * (1 + r)^3

Dividing the second equation by the first equation, we get:

(1 + r)^3 = 3676.31/3300
1 + r = (3676.31/3300)^(1/3)
r = (3676.31/3300)^(1/3) - 1

Substituting r into the first equation, we get:

3300 = P * ((3676.31/3300)^(1/3) - 1) * 3
P = 3300/((3676.31/3300)^(1/3) - 1)

Therefore, the principal is P = Rs. 10000 and the annual rate of interest is r = 0.1 or 10%.