Calculating Simple Interest Rate

This problem involves calculating the annual rate of simple interest given the time period and the relationship between the final amount returned and the original principal.

Key Information Extraction

• Time Period ($T$): 4 years
• Amount Returned ($A$) relative to Principal ($P$): $A = \frac{6}{5}P$
• Interest Type: Simple Interest
• Goal: Find Rate of Interest ($R$) per annum (p.a.)

Simple Interest Calculation Steps

First, determine the total interest earned over the 4 years.

• Interest ($SI$) = Amount ($A$) - Principal ($P$)
• $SI = \frac{6}{5}P - P$
• $SI = (\frac{6}{5} - 1)P$
• $SI = \frac{1}{5}P$

Next, use the simple interest formula:

$SI = \frac{P \times R \times T}{100}$

Substitute the known values:

• $SI = \frac{1}{5}P$
• $T = 4$ years
• $\frac{1}{5}P = \frac{P \times R \times 4}{100}$

Now, solve for the rate ($R$). We can cancel $P$ from both sides, assuming the principal is non-zero.

• $\frac{1}{5} = \frac{4R}{100}$
• $R = \frac{1}{5} \times \frac{100}{4}$
• $R = \frac{100}{20}$
• $R = 5$

Therefore, the rate of interest is 5% p.a.