Final answer:
The annual rate of simple interest on an investment that earned P 30φ in three months on a principal of P 12000 is 10%. The interest rate was calculated using the simple interest formula I = PRT rearranged to solve for the rate (R). The correct option is C. 10%.
Step-by-step explanation:
The simple interest formula is I = PRT, where I is the interest earned, P is the principal amount, R is the rate of interest per year, and T is the time in years. In the given question, to calculate the annual rate of simple interest, we will use the information that P 30φ is earned in three months on an investment of P 12000.
Since the interest is for 3 months, we need to convert the time to years by dividing by 12: T = 3/12 = 0.25 years. The interest I is P 30φ. Now we apply these values to the simple interest formula: 30φ = 12000 × R × 0.25. To solve for R, the rate of interest per year, we can rearrange the equation: R = 30φ / (12000 × 0.25). After calculation, R = 0.10 or 10%. The correct option, therefore, is C. 10%. This is the annual rate of simple interest earned on the investment.