If you pay your $3,000 tuition 3 months before it is due, the local college will give you a $250 "scholarship" reducing your tuition payment to $2,750. What is the annual simple interest rate to which this incentive is equal?
A) 36.4%
B) 9.1%
C) 8.3%
D) 33.3%
E) 27.3%

Question

Quizplus · Accepted Answer

The $250 "scholarship" for paying 3 months early is equivalent to an interest saving for not having to pay the $3,000 tuition for those 3 months. To find the annual interest rate, we calculate the interest for a year. The interest for 3 months is $250 on $3,000, which is an 8.3% rate for 3 months (250/3000 = 0.0833). To annualize this rate, we multiply by 4 (since there are 4 sets of 3 months in a year): 8.3% * 4 = 33.3%. However, the correct calculation to annualize the rate based on the incentive given for early payment should consider the opportunity cost of paying early. The correct approach is to see the $250 as an interest earned on $2,750 (since you pay this amount instead of $3,000) over 3 months, not as an interest rate on the full $3,000. The annualized rate is calculated by (250/2750) * (12/3) = 0.3636 or 36.4%.

If You Pay Your $3,000 Tuition 3 Months Before It