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%.