Final answer:
To find the annual interest rate where the simple interest for 5 years is 2/5 of the sum, we use the formula I = PRT. After rearranging and solving, we determine that the annual interest rate is 8% per annum.
Step-by-step explanation:
The student is asking about determining the annual interest rate for a sum of money when the simple interest accrued over 5 years is 2/5 of the principal sum. To calculate the simple interest rate, we can use the formula for simple interest, which is I = PRT, where:
- I is the interest,
- P is the principal amount,
- R is the rate of interest per year, and
- T is the time in years.
Given that the simple interest I is 2/5 of the principal P, and the time T is 5 years, we can rearrange the formula to solve for R (the annual interest rate).
First, we denote 2/5 of P as the interest, so I = (2/5)P. We substitute this into the formula and get:
(2/5)P = P * R * 5
After we simplify and solve for R:
R = (2/5) / 5 = 2/25
Converting the fraction to a percentage:
R = (2/25) * 100% = 8%
Thus, the annual interest rate is 8% per annum.