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%.