1)     Mrs. Smith walks into the Bank of Vancouver and notices the line up at the ATM machine.  She never used the ATM machines as she doesn’t trust the security of the pin numbers.  Stealing of pin numbers aside, she thinks it’s not hard to guess someone’s pin with a limited 4 figure, digit-only selection. Using the client card the bank gives you, you are to supply a 4 digit pin.

 

 

a.      What is the probability that a person can guess your pin? 

 

1/10 * 1/10 * 1/10 * 1/10 = 1/10,000

 

b.      If somehow, you can add the option of using alphabets also in your 4 character pin, what is the probability that a person can guess your new pin now?

 

1/36 * 1/36 * 1/36 * 1/36 = 1/1,679,616

 

c.      How many times harder is it to guess the 4 character alpha-numeric pin than it is to guess the 4 digit numeric pin?

 

1,679,616/10,000 ~ 168 times

 

 

2)     As she passes the ATM line-up, she notices a sign that says "Average wait time in this bank: Teller - 3.5 minutes ATM - 2.25 minutes". Even though Mrs. Smith needed to talk to a teller, she starts to wonder …

 

a.      If there were 5 people lining up at the ATM (adding you would be 6) and 3 people lining up at the teller (adding you would be 4), which line up would be faster? 

 

ATM: 6 * 2.25 minutes = 13.5 minutes

Teller: 4 * 3.5 minutes = 14 minutes

 

Therefore the Teller line up would be faster.

 

b.      If there were 8 people already lining up for the tellers, what is the maximum number of people lining up at the ATM for it to be faster than the teller line up? (Don't forget to include you in the wait time for both.)

 

Teller: 8 * 3.5 minutes = 28 minutes

28 minutes / 2.25 minutes = 12.4

 

Therefore if there are 12 or less people lining up at the ATM, it would be faster.

 

 

3)     There were actually 4 people lining up at for the tellers and only 2 tellers working.  Mrs. Smith was watching the bank employees at their best as they were dealing with clients at a phenomenal rate.  Since this was the case, she starts to think how many customers can be served if more tellers were added.

 

 

a.      Suppose 4 tellers can serve 60 customers in 1 hr.  Assuming that all the tellers work at the same speed, if you added another teller, how many customers will be served in the same amount of time?

 

60 customers/hour for 4 tellers, thus 60 customers/4 tellers = 15 customers/hour for each teller.

 

So if we had 5 tellers, 15 customers/hour * 5 = 75 customers/hour.  Therefore 75 customers will be served in an hour.

 

b.      Suppose: Teller A can serve 40 customers in 2 hrs. Teller A & B can serve 45 customers in 1 hr.  How many customers can Teller B serve in 1 hr?

 

Teller A: 40 customers/2 hours = 20 customers/1 hour

 

Since Teller A served 20 customers in an hour, then Teller B must have served the remaining (45 – 20) 25 customers in the same hour. Thus Teller B can serve 25 customers/1 hour.

 

 

 

 

1)     As Mrs. Smith was looking at the interest rates posted on the wall, she can’t help but reminisce about the days when she was young and the interest rate was something worthwhile. Assume the annual interest rate at the bank increased from 10.5% to 12.75%:

 

a.      What is the percentage increase?

 

12.75% – 10.5% = 2.25%

 

b.      If you had $500 in the bank, how much more interest did you receive after the first year?

 

$500 * (12.75% - 10.50%) = $11.25

 

c.      With the new and old interest rate, calculate your total investments after 5 years by filling out the table below.  Considering that it’s compounded annually and the interest rate remains the same for the 5 years. 

 

 

 

 

 

 

 

2)     Mrs. Smith’s son, Marcus, also has a bank account here.  She’s trying to save up for a post secondary education. Suppose Marcus’ account started with $2000 and every year he added an extra $1500 to it.  With the annual rate of 8.0% for the first 2 years, then 8.5% for the third, 9.0% for the forth and 10.0% for the fifth:

 

a.      What would his closing balance be after 5 years?

 

 

 

b.      What is the total interest earned?

 

$12042.14 - $2000 – ($1500 * 5) = 2542.14

 

 

3)     Mr. and Mrs. Smith actually have a loan from the bank.  They borrowed $10,000 from the bank to buy a new mini-van (currently in the shop). The agreed upon annual interest rate charged will be 7.5%.  If they can make annual payments of $1500:

 

a.      How long will it take before the Smiths completely paid back the loan?

 

 

 

b.      Calculate the total charged interest for this loan.

 

$750 + $693.75 + $633.28 + $568.28 + $498.4 + $423.28 + $342.52 + $255.71 + $162.39 + $62.07 = $4389.68

 

 

 

 

 

Country	Currency /Code	Client Buys (Pays Canadian)	Client Sells (Receives Canadian)
United States	Dollar (USD)	1.352000	1.312000
Great Britain	British Pound (GBP)	2.453400	2.379500
Australia	Dollar (AUD)	0.959300	0.895900
Switzerland	Franc (CHF)	1.072500	1.010100
Euro	Euro (EUR)	1.641700	1.563500
Hong Kong	Dollar (HKD)	0.176000	0.165700
Japan	Yen (JPY)	0.012184	0.011557

 

1)     The main reason for Mrs. Smith’s visit here was to convert her $345 USD to Canadian dollars. It was left over from her business trip to Seattle a week ago.  How much money in Canadian dollars should she receive?

 

$345 * 1.312 = $452.64

 

 

2)     Based on the buy & sell exchange rates, it appears that the bank is making money by having the clients buy currency at a higher  rate than when they are selling.  Using the Hong Kong currency as an example:

 

a.      How much money does the bank make if you bought $550 HKD, then sold it back to the bank immediately?

 

$550 * (0.176 – 0.1657) = $5.66

 

 

b.      Write an expression describing how much the bank makes if you bought $X HKD and immediately sold it back.

 

X * (0.176 – 0.1657) = 0.0103X