Mortgage payment inquiry

[Rome34]

I am currently splitting equal mortgage payments with my spouse. The mortgage is $980/month ($490 each). We are in the process refinancing to a higher interest rate and using the equity to pay off other higher interest rate debts. To do so, we are receiving $22,000 back at closing. However, I am taking 2/3 of the $22,000 ($14,667) and she will be getting the other 1/3 ($7,333) for different debts. Our new mortgage payment is estimated to be $15,444. Considering the different amount of cash back we will be splitting, what will be a fair amount for us to individually pay towards the new mortgage?

I was originally thinking I would pay 2/3 ($1,029.33), of the new mortgage payment, leaving her to pay the remaining 1/3 ($514.67). But this doesn't seem to make mathematical sense in the long-term. Please advise. Thanks!

 

[BigBeachBanana]

I am currently splitting equal mortgage payments with my spouse. The mortgage is $980/month ($490 each). We are in the process refinancing to a higher interest rate and using the equity to pay off other higher interest rate debts. To do so, we are receiving $22,000 back at closing. However, I am taking 2/3 of the $22,000 ($14,667) and she will be getting the other 1/3 ($7,333) for different debts. Our new mortgage payment is estimated to be $15,444. Considering the different amount of cash back we will be splitting, what will be a fair amount for us to individually pay towards the new mortgage?

I was originally thinking I would pay 2/3 ($1,029.33), of the new mortgage payment, leaving her to pay the remaining 1/3 ($514.67). But this doesn't seem to make mathematical sense in the long-term. Please advise. Thanks!

What's the new interest rate?

 

[blamocur]

I am currently splitting equal mortgage payments with my spouse. The mortgage is $980/month ($490 each). We are in the process refinancing to a higher interest rate and using the equity to pay off other higher interest rate debts. To do so, we are receiving $22,000 back at closing. However, I am taking 2/3 of the $22,000 ($14,667) and she will be getting the other 1/3 ($7,333) for different debts. Our new mortgage payment is estimated to be $15,444. Considering the different amount of cash back we will be splitting, what will be a fair amount for us to individually pay towards the new mortgage?

I was originally thinking I would pay 2/3 ($1,029.33), of the new mortgage payment, leaving her to pay the remaining 1/3 ($514.67). But this doesn't seem to make mathematical sense in the long-term. Please advise. Thanks!

Paying 2/3 of the mortgage does not makes sense to me: you'd end up paying off 2/3 of the whole debt. I'd treat this as if you borrowed 1/6 of $22,000 from your spouse and settle it somehow separately.

Alternatively, you could treat this as owing different parts of the principal refinanced debt, i.e., you've ended up borrowing $7333.33 more from the bank than you spouse, so you should pay proportionally larger amount of mortgage, but probably not 2/3 of it. For example, if your new principal is $200,000, then your part is one half plus $7333.33/2 =$103666.67 and your spouse's part is $96333.33. This means that your share of the mortgage payments should be $103666.67 / $200000 = [imath]\approx[/imath] 51.8333%, with your spouse paying the rest. I.e., you proportion of the mortgage payment depends on the principal. The problem with this approach is that the next time you refinance again you will have to keep track which you'll have to figure out how much you still owe to your spouse. For example, let's say that at that time the remaining principal is $100000. This means that you owe to your spouse only one half of the original debt, i.e. 1/12 of $22000 instead of 1/6 because you've paid up half of that debt with your higher mortgage payment.

Hope this helps to avoid any tension in the family

 

[Rome34]

What's the new interest rate?

6.75%

 

[Rome34]

Paying 2/3 of the mortgage does not makes sense to me: you'd end up paying off 2/3 of the whole debt. I'd treat this as if you borrowed 1/6 of $22,000 from your spouse and settle it somehow separately.

Alternatively, you could treat this as owing different parts of the principal refinanced debt, i.e., you've ended up borrowing $7333.33 more from the bank than you spouse, so you should pay proportionally larger amount of mortgage, but probably not 2/3 of it. For example, if your new principal is $200,000, then your part is one half plus $7333.33/2 =$103666.67 and your spouse's part is $96333.33. This means that your share of the mortgage payments should be $103666.67 / $200000 = [imath]\approx[/imath] 51.8333%, with your spouse paying the rest. I.e., you proportion of the mortgage payment depends on the principal. The problem with this approach is that the next time you refinance again you will have to keep track which you'll have to figure out how much you still owe to your spouse. For example, let's say that at that time the remaining principal is $100000. This means that you owe to your spouse only one half of the original debt, i.e. 1/12 of $22000 instead of 1/6 because you've paid up half of that debt with your higher mortgage payment.

Hope this helps to avoid any tension in the family

Thank you for this information! In comparison, would this simple approach work the same: The difference between new and old mortgage is $564 ($1544-$980). We both continue to pay $490 equally and that leaves the $564 added because of the refinance. I will pay 2/3 of the $564 ($376) and my spouse will pay 1/3 of the $564 ($188). This will make my total portion $866 ($490+$376) and my spouse's portion will be $678 ($490+$188).

 

[JeffM]

This is not a formal analysis, but it seems equitable to me.

Whatever the new monthly payment is (for example 1100), you pay

[math]\dfrac{1}{2} * 980 + \dfrac{2}{3} * (1100 - 980) \approx 490 + 80 = 570.[/math]
She pays

[math]\dfrac{1}{2} * 980 + \dfrac{1}{3} * (1100 - 980) \approx 490 + 40 = 530.[/math]
Note that [imath]570 + 530 = 1100.[/imath]

Here is the logic. Your original understanding was that each of you would pay 1/2 of 980. Stick with that. But now you must make a higher monthly payment. You are getting 2/3 of the benefit of the increase in debt so you should pay 2/3 of the increase in the monthly payment.

In practice, the numbers will probably end up being off by a penny. I suggest you flip for it.

 

[Rome34]

Ha! Thank you for the response.

 

[blamocur]

Below is a comparison of @JeffM's approach and mine. I am assuming that the new mortgage payment is $1,544 (the $15,444 in the original post seems to be a typo). I am also assuming that the new principal is $300,000, which would correspond to the current rates of around 6%.

According to @JeffM the difference in monthly payments should be ($1544-$980)/3 = $188, and the new shares would amount to $866 and $678 respectively.

In my approach, OPs share of the new debt is $300,000/2 + $22000/6 = $153,666.67, while their spouse owes $300,000/2 - $22,000/6 = $146,333.33. This means that the OPs share of debt is 51.22222% and their spouse's 48,77778%. This means that OP should pay $790.87 (which is 51.222222% of $1544) per month while their spouse $753.13, i.e. the difference of $37.74.
Note 1: my computation depends on the amount of the new loan because it effects the debt proportions between the spouses; the higher the principal the less the difference between their payments.
Note 2: another way to look at this is to use the interest rate on the mortgage, as @BigBeachBanana suggested. Let's use 6%: an approximate monthly payment on the $22,000 loan would be in the area of $110, which brings us to the same difference in monthly payments of around $37.

 

[Rome34]

Thank you. My apologies for the typo as yes the mortgage payment will be $1,544. Also the principal will roughly be $200,000 as opposed to $300,000.

 

[blamocur]

Thank you for this information! In comparison, would this simple approach work the same: The difference between new and old mortgage is $564 ($1544-$980). We both continue to pay $490 equally and that leaves the $564 added because of the refinance. I will pay 2/3 of the $564 ($376) and my spouse will pay 1/3 of the $564 ($188). This will make my total portion $866 ($490+$376) and my spouse's portion will be $678 ($490+$188).

I still think you would be paying too much -- see my post # 8. I.e., just consider that you borrowed $7333 more than you spouse, figure out the exact amount each of you have borrowed and split the payments proportionally to your debt amounts.

 

[JeffM]

Below is a comparison of @JeffM's approach and mine. I am assuming that the new mortgage payment is $1,544 (the $15,444 in the original post seems to be a typo). I am also assuming that the new principal is $300,000, which would correspond to the current rates of around 6%.

According to @JeffM the difference in monthly payments should be ($1544-$980)/3 = $188, and the new shares would amount to $866 and $678 respectively.

In my approach, OPs share of the new debt is $300,000/2 + $22000/6 = $153,666.67, while their spouse owes $300,000/2 - $22,000/6 = $146,333.33. This means that the OPs share of debt is 51.22222% and their spouse's 48,77778%. This means that OP should pay $790.87 (which is 51.222222% of $1544) per month while their spouse $753.13, i.e. the difference of $37.74.
Note 1: my computation depends on the amount of the new loan because it effects the debt proportions between the spouses; the higher the principal the less the difference between their payments.
Note 2: another way to look at this is to use the interest rate on the mortgage, as @BigBeachBanana suggested. Let's use 6%: an approximate monthly payment on the $22,000 loan would be in the area of $110, which brings us to the same difference in monthly payments of around $37.

Below is a comparison of @JeffM's approach and mine. I am assuming that the new mortgage payment is $1,544 (the $15,444 in the original post seems to be a typo). I am also assuming that the new principal is $300,000, which would correspond to the current rates of around 6%.

According to @JeffM the difference in monthly payments should be ($1544-$980)/3 = $188, and the new shares would amount to $866 and $678 respectively.

In my approach, OPs share of the new debt is $300,000/2 + $22000/6 = $153,666.67, while their spouse owes $300,000/2 - $22,000/6 = $146,333.33. This means that the OPs share of debt is 51.22222% and their spouse's 48,77778%. This means that OP should pay $790.87 (which is 51.222222% of $1544) per month while their spouse $753.13, i.e. the difference of $37.74.
Note 1: my computation depends on the amount of the new loan because it effects the debt proportions between the spouses; the higher the principal the less the difference between their payments.
Note 2: another way to look at this is to use the interest rate on the mortgage, as @BigBeachBanana suggested. Let's use 6%: an approximate monthly payment on the $22,000 loan would be in the area of $110, which brings us to the same difference in monthly payments of around $37.

With respect to Note 1, the situation originally described contemplated a new balance due of x + 22000, which should be divided by your method into two balances of 0.5x + 14667 and 0.5x + 7333. If indeed the new mortgage is for 300000, meaning the old mortgage was for 278000, which implies that the husband owes 139000 + 14667 = 153667 and the wife owes 139000 +7333 = 146333. I agree. You then say that the husband owes only 153667/300000 = 51.2% of that debt and so should pay 1544 * 0.512 = 790.53 whereas the wife should pay 753.47 for a difference of just 37.

But as you acknowldge in your note, that result is sensitive to the assumption that the balance on the old mortgage was 278000. According to the OP, the actual amount on the old mortgage was 178000. This leads to balances of 103,667 for the husband and 96333 for the wife. The shares are now 51.8% or 799.79 and 48.2% or 744.21 for a difference of 55.

That, however, still does not account for the difference in my estimate and yours. What does?

Almost certainly it is amorization. I will bet dollars to doughnuts that the payment period has been extended on the new mortgage relative to the old mortgage. What was once say a mortgage with 18 years to run has now turned into a mortgage with 30 years to run. That is reflected in a change in the monthly payment that does not reflect the change just in the balance due, or just in the changed interest rate, or the just in the changed amortization period. I suspect that your method does not reflect an undisclosed change in amortization period, but I admit I have not done the math to prove it.

What gives my suspicion greater weight is that your Note 2 does not seem to reflect any amortization at all. Mortgage payments initially are almost all amortization.

This is not to say that you are wrong; I have not done the math. But the change in the payment amount probably reflects better the change in net benefit received and all the factors involved than just focusing on the differences in debt.

 

[Rome34]

Thank you both. Just to clarify more exactly, the old mortgage is $168, 929 and the new refinanced mortgage will be $201,600.

In addition, the old interest rate is 2.99% and the new will be 6.75%.

I greatly appreciate the input and assistance from you both!

 

[Rome34]

Also, this will be a 30 year loan...which was the same as the previous mortgage that we've had for 6 years. Thanks again

 

[blamocur]

I suspect that your method does not reflect an undisclosed change in amortization period,

Your suspicion is correct. But I don't see why the old mortgage matters at all: it all boils down to who owes what in the new mortgage, after which the payments are split proportionally.

 

[BigBeachBanana]

I haven't done a formal analysis, so just throwing something out here.

We can consider it as 2 separate loans 22,000 and 200,000. Based on the numbers provided, it should take you about 13 months to pay off 22,000 together. Since you got 2/3 utility out of the 22,000, you should pay 2/3 of the monthly mortgages for the first 13 months. Then split half thereafter.

 

[Rome34]

I haven't done a formal analysis, so just throwing something out here.

We can consider it as 2 separate loans 22,000 and 200,000. Based on the numbers provided, it should take you about 13 months to pay off 22,000 together. Since you got 2/3 utility out of the 22,000, you should pay 2/3 of the monthly mortgages for the first 13 months. Then split half thereafter.

Interesting take that I haven't considered. Thank you as well.

 

[BigBeachBanana]

This is another approach and something I would personally do. Allocate the payments based on the loan amount and utility.

Loan 1 allocation = [imath]\dfrac{22,000}{222,000} = 9.91\%[/imath]
Loan 1 allocated payment = [imath]1,544 \times 9.91\% = 153.01[/imath]
Husband's share =[imath] \dfrac{2}{3} \times 153.01 = 102.01[/imath]
Wife's share =[imath] \dfrac{1}{3} \times 153.01 = 51.00 [/imath]

The calculation is similar for Loan 2. Each person's monthly share is in orange with the difference of 51.

 

[Rome34]

Thank you again. Wow. It appears there may be multiple different approaches to this inquiry. But the one constant is that I was truly way off with my original approach. Ha!

 

[blamocur]

View attachment 34997

This is another approach and something I would personally do. Allocate the payments based on the loan amount and utility.

Loan 1 allocation = [imath]\dfrac{22,000}{222,000} = 9.91\%[/imath]
Loan 1 allocated payment = [imath]1,544 \times 9.91\% = 153.01[/imath]
Husband's share =[imath] \dfrac{2}{3} \times 153.01 = 102.01[/imath]
Wife's share =[imath] \dfrac{1}{3} \times 153.01 = 51.00 [/imath]

The calculation is similar for Loan 2. Each person's monthly share is in orange with the difference of 51.

Using my approach for the total amount of $220,000 yields the same difference of $51 (and for the actual amount of $201,600 it should be $56.16). I.e., I think our approaches are equivalent.

But there is an important caveat about amortization mentioned by @JeffM: if, say, 5 years from now you refinance again or decide to pay off the current mortgage in other ways you will still owe your spouse a pretty large chunk of those $22000/6 = $3666.67 since most of the payments in the first years go to pay the interest, not the principal. The remaining principal will have to be divided proportionally, i.e. if the remaining principal is [imath]P[/imath] you will owe ($201,600/2 + $3666.67) / $201,600 share, i.e. 0.51819*P with your spouse owing the remaining 0.48181*P.

Hope this is more helpful than confusing

 

[Rome34]

Using my approach for the total amount of $220,000 yields the same difference of $51 (and for the actual amount of $201,600 it should be $56.16). I.e., I think our approaches are equivalent.

But there is an important caveat about amortization mentioned by @JeffM: if, say, 5 years from now you refinance again or decide to pay off the current mortgage in other ways you will still owe your spouse a pretty large chunk of those $22000/6 = $3666.67 since most of the payments in the first years go to pay the interest, not the principal. The remaining principal will have to be divided proportionally, i.e. if the remaining principal is [imath]P[/imath] you will owe ($201,600/2 + $3666.67) / $201,600 share, i.e. 0.51819*P with your spouse owing the remaining 0.48181*P.

Hope this is more helpful than confusing

I'm definitely no Will Hunting, but I feel I have a better handle on the eventual solution thanks to the help of you all.