Question

The difference between the compound interest and simple interest on a certain sum for 2 years at 6% per annum is ₹ 90. Find the sum.

Answer 1

Given:

Interest rate= 6% per annum

Time=2 years

Simple interest (SI) = PTR/100

Where P is principle amount, T is time taken, R is rate per annum

Let sum is P

SI = (P × 2× 6)/ 100

⇒ SI = (12P)/ 100

⇒ SI = (3P)/ 25 —————- equation 1

To find the amount we have the formula,

Amount (A) = P (1+(R/100))ⁿ

Where P is present value, r is rate of interest, n is time in years.

Now substituting the values in above formula we get,

∴ CI= P (1 + 6/100)²-P

⇒ CI = P (1+3/50)²-P

⇒ CI = P (53/50)²-P

⇒ CI = P (2809) / (2500) – P

⇒ CI = 309P/2500——– equation 2

Now the difference is

(CI – SI) = 309P/2500 – (3P)/ 25

⇒ 90 = 309P/2500 – (3P)/ 25

⇒ 90 = 309P – (300P)/2500

⇒ 90 = 9P/2500

⇒ P= 90 × 2500/9

⇒ P= 10 × 2500

⇒ P=25000

∴ Sum = 25000