Shortcut Trick
For consecutive years, the rate of interest is calculated on the previous year's amount.
Rate % = [(Difference in Amounts) ÷ (Initial Amount)] × 100
Rate % = [(2,977.54 − 2,809) ÷ 2,809] × 100
Rate % = [168.54 ÷ 2,809] × 100 = 6%
∴ The correct answer is 6%.
Alternate Method
Given:
Amount after 2 years (A2) = ₹2,809
Amount after 3 years (A3) = ₹2,977.54
Formula Used:
In compound interest, A = P(1 + R/100)n. For consecutive years, An+1 = An(1 + R/100).
Calculations:
⇒ Interest for the 3rd year = A3 − A2
⇒ Interest = 2,977.54 − 2,809 = 168.54
⇒ This interest is earned on the principal of ₹2,809 (which is the amount at the end of year 2).
⇒ Rate (R) = (Interest ÷ Principal) × 100
⇒ R = (168.54 ÷ 2,809) × 100
⇒ R = 16854 ÷ 2809
⇒ R = 6%
∴ The correct answer is 6%.
Additional Information
Compound Interest Formula
The amount A after n years is given by A = P(1 + R/100)n, where P is the principal and R is the annual rate.
Successive Percentage Change
Compound interest is essentially a successive percentage increase. For two years, the effective rate is x + y + (xy/100).
Difference between CI and SI
For 2 years, the difference between CI and SI is P(R/100)2.