What is the correct way to calculate the amount of money to receive in 4 months when the total amount to receive in 1 year is 17500?

Question

I am still at college. I need to solve this problem.

The total amount to receive in 1 year is 17500 CAD. And the university pays its students each 2 weeks (26 payments per year).

How much does a student have to receive for 4 months? I have calculated this in 2 ways (both seem ok) but results are different. Which one is the right one and why?

a) 17500CAD / 12 months = 1458.33CAD each month
   1458.33CAD x 4 months = 5833 (total amount of money in 4 months)

   If money has to be given each 2 weeks: 
   5833 / 8 = 729.125 CAD 

b) 17500 / 26 = 673.08 each 2 weeks 
   673.08 x 8 = 5384.62 (total amount of money in 4 months)

I think the right one is a), because b) is assuming the student has been receiving money for the whole year (26 payments). But it is not the case.

Thank you

Answer 1

a) assumes 4 weeks per 12 months, which is equivalent to a 48-week year.

b) assumes a 52-week year.

Given that the question explicitly relates payments to "weeks", the second convention seems preferable. The correct answer (in my opinion) is b).

Answer 2

There are more than $8$ two week periods in four months. If you are paid by the month, the first calculation is correct and the total should be $5833$. On average there are $17$ weeks (and a little) in four months so you would get eight full two week paychecks and one more smaller one. The checks will be smaller than the $729.125$ you calculate. Your second calculation assumes a $364$ day year. If you account for the extra week you will be very close to the first approach.

Answer 3

Okey. This is my solution:

1 year = 365 days or 366 days

two-week period = 14 days

365 / two-week period = 26 payments per year

September to December = 122 days

122 / two-week period = 8.71 payments



(175000 / 26) x 8.71 = 5863 CAD

Answer 4

If you consider that a month has $4$ weeks, you have a total of $48$ weeks, not $52$.