The difference between the compound interest and the simple interest accrued on an amount of ₹40,000 in 2 years was ₹324. The rate of interest per annum was:
9%
Given:
Compound Interest (CI) - Simple Interest (SI) = 324
Principal = 40000, Time = 2 years
Used formula:
Compound Interest = Total Amount - Principal
CI = P[(1 + R/100)n - 1]
Simple Interest = (P × R × T)/100
Calculation:
According to the question:
⇒ P[(1 + R/100)n - 1] - (P × R × T)/100 = 324
⇒ 40000 [(1 + R/100)2 - 1] - (40000 × R × 2)/100 = 324
⇒ 40000 [{(100 + R)2/1002 - 1} - {R × 2}/100 = 324
⇒ 400 [{1002 + R2 + 2 × 100 × R - 1002}/100 - 2R] = 324
⇒ [{R2 + 200R}/100 - 2R] = 324/400
⇒ (R2 + 200R - 200R)/100 = 324/400
⇒ R2 = 32400/400
⇒ R2 = 81 = 9%
∴ The rate of interest per annum is 9%.
Used formula:
Shortcut Trick
For 2 years, the difference between CI and SI,
⇒ D = P(R/100)2
Where,
D = difference, P = principal, R = rate of interest
Calculation:
⇒ 324 = 40000(R/100)2
⇒ R2 × 40000 = 3240000
⇒ R2 = 81
⇒ R = 9%
∴ The desired rate of interest is 9%.
Important Questions from Simple and Compound Both
If the compound interest on a certain sum of 2 years at 4% per annum is ₹1530. What would be the simple interest on the same sum for the same period and at the same rate?
There is 70% increase in an amount in 7 years at simple interest. What will be the compound interest on ₹8,000 after 3 years at the same rate of interest?
The difference between the compound interest and the simple interest on a certain sum at 8% per annum for 2 years is ₹144. What is the amount (in ₹)?
The difference between the compound interest and the simple interest on a certain sum at 5% per annum for 2 years is ₹152. What is the amount (in ₹)?
The Difference between compound interest, compounding annually and simple interest on an amount of ₹500 for 2 years is ₹1.25. What is the rate of interest per annum?
