If a sum of money at a certain rate of simple interest per year double...
Interest/Principal = Rate/100 × Time
In first case, Amount gets double
∴ Interest = Principal
1 = Rate/100 × 5
∴ Rate = 20%
In second case, amount gets tripled
∴ Interest = 2 × Principal
2 = Rate/100 × 12
∴ Rate = 50/3%
Difference = 20 - 50/3 = 10/3%
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If a sum of money at a certain rate of simple interest per year double...
Let's assume the initial principal amount as P and the rate of interest for the first case as R1 and for the second case as R2.
Case 1: Doubling in 5 years
According to the question, the sum of money doubles in 5 years at a certain rate of simple interest per year. This means that after 5 years, the amount becomes 2P.
Using the formula for simple interest, we can write the equation as:
2P = P + (P * R1 * 5)
Simplifying the equation, we get:
P * R1 * 5 = P
Dividing both sides by P, we get:
R1 * 5 = 1
Therefore, the rate of interest for the first case is R1 = 1/5 or 20%.
Case 2: Becoming three times in 12 years
According to the question, the sum of money becomes three times in 12 years at a different rate of simple interest per year. This means that after 12 years, the amount becomes 3P.
Using the formula for simple interest, we can write the equation as:
3P = P + (P * R2 * 12)
Simplifying the equation, we get:
P * R2 * 12 = 2P
Dividing both sides by P, we get:
R2 * 12 = 2
Therefore, the rate of interest for the second case is R2 = 2/12 or 1/6 or 16.67%.
Difference in the rates of interest
The difference in the rates of interest can be calculated as:
Difference = R1 - R2 = 20% - 16.67% = 3.33%
Converting the difference to a fraction, we get:
Difference = 3.33/100 = 10/3%
Therefore, the difference in the two rates of simple interest per year is 10/3%.