To calculate the rate of simple interest, we can use the formula:
Simple Interest (SI) = Principal (P) * Rate (R) * Time (T)
Where:
- Principal (P) is the initial amount of money
- Rate (R) is the interest rate (in decimal)
- Time (T) is the time period (in years)
We can rearrange the formula to solve for the interest rate (R):
Rate (R) = (Simple Interest (SI) / Principal (P)) / Time (T)
Let's calculate the rates for each scenario:
a) For $1000 accumulating to $1420 in 2.5 years:
SI = $1420 - $1000 = $420
Rate (R) = (420 / 1000) / 2.5 = 0.168 or 16.8%
b) For money to double itself in 8 years:
Here, the final amount is twice the initial amount, so the simple interest earned is equal to the principal amount.
SI = $1000
Rate (R) = (1000 / 1000) / 8 = 0.125 or 12.5%
c) For $500 accumulating $10 interest in 2 months:
First, we need to convert the time period to years:
2 months = 2/12 = 1/6 years
SI = $10
Principal (P) = $500
Time (T) = 1/6 years
Rate (R) = (10 / 500) / (1/6) = (1/50) / (1/6) = (6/50) = 0.12 or 12%
Therefore, the rates of simple interest are:
a) 16.8%
b) 12.5%
c) 12%
