A sum of money, on compound interest, amounts to ₹578.40 in 2 years and to ₹614.55 in 3 years. The rate of int

Question

A sum of money, on compound interest, amounts to ₹578.40 in 2 years and to ₹614.55 in 3 years. The rate of interest per annum, in case of annual compounding, is:

Examoogle · Accepted Answer

The correct answer is Option B: $6\frac{1}{4}\%$. Finding Annual Compound Interest Rate from Successive Year Amounts

Step-by-Step Solution & Concepts:
Key Fact: Finding Annual Compound Interest Rate from Successive Year Amounts

Given: Amount after 2 years $A_2 = ₹578.40$, Amount after 3 years $A_3 = ₹614.55$

Key Formulas: $r = \frac{A_{n+1} - A_n}{A_n} 	imes 100\%$

Key Points: No need to calculate the initial Principal $P$.; $6.25\%$ converts exactly to mixed fraction $6\frac{1}{4}\%$.

Steps: Determine 1-Year Compound Interest: In annual compound interest, the amount at the end of the 2nd year acts as the principal for the 3rd year. Thus, the interest earned in the 3rd year is: $$	ext{Interest} = A_3 - A_2 = 614.55 - 578.40 = ₹36.15$$. Calculate Annual Rate of Interest: $$r = \frac{	ext{Interest}}{A_2} 	imes 100 = \frac{36.15}{578.40} 	imes 100$$ $$r = \frac{3615}{578.4} = 6.25\% = 6\frac{1}{4}\%$$

Answer: Option B is correct — 6¼%

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)