The formula for simple interest is:
I = P·R·T
Since R is the interest rate per year, we must convert the time (T) to years. We must also convert the rate to decimal. For I = $84, R = 8% = 0.08, T = 3 months = 3/12 = 0.25 year:
$84 = P·(0.08)·(0.25)
$84 = P·(0.02)
$84/(0.02) = P
$4200 = P
For P = $1500, I = $138, T = 2 years:
$138 - ($1500)·R·(2 years)
$138 = $3000·R
Solve for R. R will be in decimal form. To convert to %, multiply by 100%.