If the cost of going to the ATM is $2 and the nominal interest rate is 1 percent, someone who has a 9 percent probability of having his cash lost or stolen and spends $15 each day will go to the ATM once in every ____ days approximately.
A)25
B)31
C)37
D)43

Question

If the cost of going to the ATM is $2 and the nominal interest rate is 1 percent, someone who has a 9 percent probability of having his cash lost or stolen and spends $15 each day will go to the ATM once in every ____ days approximately. 
A)25
B)31
C)37
D)43

Quizplus · Accepted Answer

First, we need to calculate the expected cost of going to the ATM in one day:
Expected cost = probability of loss/theft * cost of cash + cost of ATM fee
Expected cost = 0.09 * $15 + $2
Expected cost = $3.35

Next, we need to calculate how many days it will take for the nominal interest earned (1%) to offset the expected cost of going to the ATM each day ($3.35) using the formula:
Years to break even = ln(expected cost per day / interest earned per day) / ln(1 + interest rate)

Days to break even = (ln(expected cost per day / interest earned per day) / ln(1 + interest rate)) * 365

Days to break even = (ln($3.35 / ($15 * 0.01)) / ln(1 + 0.01)) * 365
Days to break even ≈ 31
Therefore, someone who has a 9 percent probability of having his cash lost or stolen and spends $15 each day will go to the ATM once in every approximately 31 days to break even on the expected cost of going to the ATM each day with the nominal interest earned. Choice B is the best choice, which shows the closest value to 31.

If the Cost of Going to the ATM Is $2