The difference between the compound interest and simple interest on a

1.	The difference between the compound interest and simple interest on a certain sum for 3 years at 10% per annum is ₹ 93. Find the sum.
Answer» Given: Interest rate= 10% per annum Time=3 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 × 3× 10)/ 100 ⇒ SI = (30P)/ 100 ⇒ SI = (3P)/ 10 —————- 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 + 10/100)³-P ⇒ CI = P (1+1/10)³-P ⇒ CI = P (11/10)³-P ⇒ CI = P (1331) / (1000) – P ⇒ CI = 331P/1000——– equation 2 Now the difference is (CI – SI) = 331P/1000 – (3P)/ 10 ⇒ 93 = 331P- 300P/1000 ⇒ 93 = 31P/1000 ⇒ P= 93 × 1000/31 ⇒ P= 3 × 1000 ⇒ P= 3000 ∴ Sum = ₹3000

The difference between the compound interest and simple interest on a certain sum for 3 years at 10% per annum is ₹ 93. Find the sum.

Answer»

Given:

Interest rate= 10% per annum

Time=3 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 × 3× 10)/ 100

⇒ SI = (30P)/ 100

⇒ SI = (3P)/ 10 —————- 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 + 10/100)³-P

⇒ CI = P (1+1/10)³-P

⇒ CI = P (11/10)³-P

⇒ CI = P (1331) / (1000) – P

⇒ CI = 331P/1000——– equation 2

Now the difference is

(CI – SI) = 331P/1000 – (3P)/ 10

⇒ 93 = 331P- 300P/1000

⇒ 93 = 31P/1000

⇒ P= 93 × 1000/31

⇒ P= 3 × 1000

⇒ P= 3000

∴ Sum = ₹3000