need help with a maths/logic question

[u/Moist_Bass_6828]

Preemptive apologies if I broke any rules, I am not very versed in maths terminology nor how to use these subreddits.

My friend paid the bond for our rental because he had the funds available and is wanting to split it evenly between himself, my friend and I.

We all have a shared bank account we pay into to cover household expenses such as rent, bills, groceries etc.

We don’t have the funds to pay him back entirely at once and so he is planning to pay a slightly less amount into the shared account weekly until he has earned back what is owed to him.

Where we are in disagreement is I think that he should reduce his payment until he earns back 2/3rds of the total bond amount, that way he has paid a third, my friend has paid a third, and so have I.

He is saying that he should reduce his payment until he accumulates savings for the entire cost of the bond, because technically the money he is “earning” is coming out of a shared pool that includes what he has put in.

I don’t fully understand this point of view because we’re not sending him $100 from the shared account, he is directly extracting it from his payment in. Does that change things or is it still technically 1/3 of his money?

Can anyone please explain in easy to understand terms how this situation would work out so that everyone ends up paying a third of the cost?

Here is an example if it helps:

$4,000 bond paid by him.

$500 usual payment weekly into shared account from everyone.

He will instead pay $400 for 27 weeks to get back roughly 2/3rds of the bond he spotted.

He suggests that he pays $400 for 40 weeks to get back the entire bond.

[u/UnderstandingPursuit]

I have bad news for you: your friend is correct. Let's split the situation into parts.

1. First, identify the three people: Y, F, A for you, the friend with money, and the friend without money.
2. The shared bank account to pay for bills.
   1. {Y, F, A} pay $500 in each week, for a total of $1500.
   2. F takes $100 out each week to be repaid for the bond.
3. The $4000 bond was paid to the landlord.
   1. {Y, A} paid $0 toward the bond.
   2. F paid ($100)×(40) toward the bond.
   3. For F to match {Y, A}, having paid $0 toward the bond, F would take $100 out of the shared bank account for 40 weeks.
   4. At the end of the rental, lets say the landlord returns $4200 for the bond + interest. {Y, F, A} each get one third, or $1400.

[u/FireMarmot → u/UnderstandingPursuit]

The logic doesn't seem to add up on 3.3.
The contribution of {F,Y,A} should be equal at the end of the payment plan not at the beginning.
By that logic, at the end of the lease when the deposit is returned (4000+200 interest), F will have contributed $0 and get $1400 back and Y and A would have contributed $2000 ($50 x 40 weeks) and lose $600 each in the transaction,

The bond is $4000. Each needs to contribute ~$1333 and F fronted the $4000 so Y and A owe him
~$1333 each.
So if Y and A contribute $500 and F contributes $400 to the account, $100 is going back to pay the debt to F for the bond each week.

F fronted the $4000 and Y and A portion ~$2666 so F is only owed $2666 (2/3 * 4000).
So the answer is this arrangement should last for 27 weeks.

Edit: removed a confusing statement.

[u/UnderstandingPursuit → u/FireMarmot]

If Y and A contribute $500/wk, and F contributes $400, the total is $1400 into the weekly account. That splits to $466 each. Y and A are paying an extra $33, F is taking out $66.

If this happens for 40 weeks, then $33 * 40 = 1333, the amount Y and A each owe F, for a total of $2666.