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Homework answers / question archive / Sarah Truman is an avid scuba diver who lives in Maine
Sarah Truman is an avid scuba diver who lives in Maine. Since New England waters are very cold, Sarah has decided to purchase a dry suit for diving. After some investigation, Sarah must decide which one of the two suits to buy - a "Denmark" suit for $750 or a "Washington" suit for $300. The major difference between the two is that the Denmark should last for 300 dives whereas the Washington suit will need to be replaced after 100 dives. Sarah has $750 in a savings account paying 8% interest, which can be used to pay for either suit. Which suit would be the most economical for Sarah to buy? Analyze Sarah's problem for each of the following assumptions:
-Sarah expects to make 25 cold water divers per year for the next 12 years.
-Sarah expects to make 50 cold water divers per year for the next 6 years.
Answer:
Per year dives = 25
No.of Years = 12
Total Dives = 300
Replacement Period (Washington) = 100/25 = 4 ; Every 4 year need to replace Denmark
Replacement Period (Denmark) = 300/25 = 12 ; Every 12 year , or no need to replace for this situation.
If bought Washington SUIT for $300 , Balance $450 in bank earning 8% interest until next replacement
ie, After 4 years balance in bank = (1.08^4)*450 = $612.22
Second Replacement , Balance in bank = $612.22 - $300 =$312.22 earning 8% for another 4 years
ie, After total 8 years, balance in bank = $312.22*(1.08)^4 = $424.77
3rd and Final Replacement , Balance in Bank = $424.77 - $300 = $124.77
So it is better to buy Washington Suit for $300 , because if bought denmark for $750 , there wont be any balnce in the bank but for Washington , there would be $124.77 balance.
Case 2 ,
Per Dives = 50,
No.of years = 6
total dives = 300,
Replacement period = 100/50 = 2 , Washington Suit lasts for 2 years, whereas Denmark suits lasts 300/50 = 6 years. (no need of replacement)
If bought Washington , Balance = $450 , in two years earnings from bank = (1.08^2)*450 = 524.88
After 2 years , replacement , balance = 524.88-300 = $224.88 , earnings for another 2 years = (1.08^2)*224.88=262.3 , so after 4 years bank balance would be only $262.3 , it is insufficient for buying another suit, so better buy DENMARK suit for $750 at the beginning.
