Sam is considering starting a healthy life style this year and is looking to joi
ID: 349151 • Letter: S
Question
Sam is considering starting a healthy life style this year and is looking to join the local gym for the coming 10 months. He can choose between two plans A or B. In Plan A, the gym charges a sign-up fee of $120 and $30 per month, while in Plan B, there is no sign-up fee but the monthly fee is $45. Answer the following and show your analysis
a) Help Sam make a decision on which plan to choose? Show your work
b) After how many months would both plans become indifferent? Show your work
c) Suppose Sam saw a coupon that costs $10 and will give him a discount of $5/month for the first 6 months of being enrolled in Plan B. Should he purchase the coupon? Justify your answer and show your work
Explanation / Answer
a) Help Sam make a decision on which plan to choose? Show your work
PLAN -A
=$120 + (10 * $30)
= $420
PLAN -B
=(10 * $45)
= $450
b) After how many months would both plans become indifferent? Show your work
After 8 months both plans would become indifferent-
PLAN -A
=$120 + (8 * $30)
= $360
PLAN -B
=(8 * $45)
= $360
c) Suppose Sam saw a coupon that costs $10 and will give him a discount of $5/month for the first 6 months of being enrolled in Plan B. Should he purchase the coupon? Justify your answer and show your work
No, Sam should not purchase the coupon, because,
PLAN -A (would remain same)
=$120 + (10 * $30)
= $420
PLAN -B (After buying coupon)
= $10 + (6 * $40) + (4 * $45)
= $430
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