The nominal rate on sarah’s loan is 7.250%. if the interest is compounded monthly, what rate of interest is sarah actually paying? a. 7.250% b. 7.496% c. 7.510% d. 8.700%

The effective annual rate (r') is ...

r' = (1 + r/12)¹² -1 = (1 +.0725/12)¹² -1 ≈ 1.0749583 -1

r' ≈ 7.496% . . . . . matches selection b.

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).