Question

8) The professor of a mechanical engineering course wishes to give each of 40 students a holiday gift. The amount needed to invest weekly for eight weeks at 26% nominal interest rate, compounded weekly,SO that each student will receive a $40 Jamba Juice gift card is nearest to a) $148 b) $164 c) $180 d) $198

Answer 1

Answer

• Points to remember.
• Amount (one of the option) is to be invested weekly.
• Total Students = 40
• Total amount needed for gift card after 8 weeks = 40 students x $ 40 card = $ 1,600
• 26% is annual interest for 365 days.
  Per day Interest rate = 26/365 = 0.07%
  Weekly Interest rate = 0.07 x 7 days = 0.49%
• CORRECT ANSWER = Option ‘D’ $ 198 is to be invested weekly.
• Verification of answer:

Week #	Beginning balance of Investment	Amount invested	Total Investment	Interest at 0.49%	Ending balance of Investment
	[A]	[B]	[C = A + B]	[D = C x 0.49%]	[E = C + D]
1	$                                               -	$                      198	$                     198	$                   0.97	$                     199
2	$                                            199	$                      198	$                     397	$                   1.95	$                     399
3	$                                            399	$                      198	$                     597	$                   2.92	$                     600
4	$                                            600	$                      198	$                     798	$                   3.91	$                     802
5	$                                            802	$                      198	$                 1,000	$                   4.90	$                 1,005
6	$                                        1,005	$                      198	$                 1,203	$                   5.89	$                 1,209
7	$                                        1,209	$                      198	$                 1,407	$                   6.89	$                 1,413
8	$                                        1,413	$                      198	$                 1,611	$                   7.90	$                 1,619

--Investing $ 198 weekly will give $ 1619 aprrox at the end of 8 week period, which is near around the money needed to provide for 40 students gift card at $ 40 each [$ 1600]