What is the annual rate of interest required for $1,835 to earn $70.59 in 346 days?
What is the calculation to determine the annual rate of interest needed for $1,835 to earn $70.59 in 346 days?
The annual rate of interest needed for $1,835 to earn $70.59 in 346 days is approximately 4.06%. To calculate the annual rate of interest, we can use the formula for simple interest: Interest = Principal × Rate × Time. Given the values: Principal ($1,835), Interest ($70.59), and Time (346 days), we can rearrange the formula to solve for Rate (R). By substituting the values and performing the calculations, we find that the rate is approximately 4.06%.
Calculation for Annual Rate of Interest:
Principal (P): $1,835
Interest (I): $70.59
Time (T): 346 days
First, let's convert the time from days to years. Since there are 365 days in a year, we divide 346 by 365:
Time (T): 346 days ÷ 365 days/year ≈ 0.949 years
Now, we can use the formula for simple interest to find the rate (R):
Rate (R) = Interest / (Principal × Time)
Substitute the given values into the formula:
Rate (R) = $70.59 / ($1,835 × 0.949)
Calculate the rate:
Rate (R) ≈ $70.59 / $1,739.915
Rate (R) ≈ 0.0406
To convert this to a percentage, multiply by 100:
Rate (R) ≈ 0.0406 × 100
Rate (R) ≈ 4.06%
In conclusion, the annual rate of interest required for $1,835 to earn $70.59 in 346 days is approximately 4.06%.