If $420 yields $31 in simple interest over 30 months, what is the annual rate?
I = PRT
31 = 420 * R * 2.5
31 = 1050R
31/1050 = R
0.0295 = R
Rate = 2.95%
To find the annual rate, we first need to determine the interest rate per month, and then convert it to an annual rate.
The formula for simple interest is:
Simple Interest = Principal * Rate * Time
In this case, we are given that the principal (initial amount) is $420, the interest is $31, and the time period is 30 months. We need to find the rate.
Let's rearrange the formula to solve for Rate:
Rate = Simple Interest / (Principal * Time)
Rate = $31 / ($420 * 30 months)
Now we can calculate the rate:
Rate = $31 / $12,600
Rate ≈ 0.00246
To convert this monthly rate into an annual rate, we multiply it by 12 since there are 12 months in a year:
Annual Rate ≈ 0.00246 * 12
Annual Rate ≈ 0.0295
Therefore, the annual rate is approximately 2.95%.