This is a simple interest problem. We need to find the rate of interest at which a principal amount doubles in 16 2/3 years.
Step 1: Understand the Formula
The formula for simple interest is: Simple Interest (SI) = (P × R × T) / 100
Where:
- P = Principal amount
- R = Rate of interest per annum
- T = Time in years
Step 2: Set up the Equation
Since the money doubles, the Simple Interest (SI) will be equal to the Principal (P). The time is given as 16 2/3 years, which is equal to 50/3 years.
Therefore, we can write the equation as:
P = (P × R × (50/3)) / 100
Step 3: Solve for R
We can simplify the equation by cancelling out 'P' from both sides:
1 = (R × (50/3)) / 100
Now, solve for R:
100 = R × (50/3)
R = (100 × 3) / 50
R = 6
Step 4: State the Answer
Therefore, the rate of simple interest is 6% per annum.
Step 5: Eliminate Incorrect Options
- 4% and 5%: If the rate were 4% or 5%, the principal amount wouldn't double in 16 2/3 years. A higher interest rate is needed.
- 6 2/3 %: This rate would cause the principal to double in less than 16 2/3 years.
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