# 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?

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

• Doesn't this depend on exactly how many two-week periods are in $4$ months? Using $4$ weeks per month, there are approximately $16$ weeks, which is $8$ pay periods, which gives $$\frac{8}{26} \cdot 17500 \approx 5385$$ However, $4$ weeks per month is an underestimate, since all months (except February on non-leap-years) have more than $28$ days. So in $4$ months you should get a bit more than $5385$, probably around $5800$. Another way to estimate is to say that $4$ months is $1/3$ of a year, so we can simply divide the total annual amount by $3$: $$\frac{17500}{3}\approx 5833$$ – Zubin Mukerjee Oct 7 '17 at 15:03
• Wow. you have given me the solution. Post it as an answer. – Aizzaac Oct 7 '17 at 16:32

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.

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).

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


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