### Author Topic: Calculating ideal payments for student loans with different interest rates  (Read 3414 times)

#### annabanana489

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##### Calculating ideal payments for student loans with different interest rates
« on: July 04, 2016, 09:38:04 AM »
Hello! I just started reading the MMM blog a few weeks ago, and am inspired to optimize my financial planning for the next couple of years.

I currently have two student loans with different interest rates and, of all the loan calculators out there, I couldn't find one to answer this question: How should I divide my payment between a 21,501.00 loan at 5.16% interest and a 20,653 loan at 5.9% interest? For example, if I have \$1,000.00 to put towards loans each month, how much should go towards each loan?

I appreciate your help!

#### Sibley

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #1 on: July 05, 2016, 09:46:29 AM »
Have you looked into refinancing to combine & potentially reduce the rate? It may not be a good idea depending on your situation, but you should research it. Cases where it's a bad idea: losing benefits that you are or plan to use, etc. Assuming it's a good idea to refi and you do that, then problem is solved and hopefully with a lower interest rate. Go forth and hammer debt.

Otherwise, given that the amounts and rates are so close, I'd probably just split it evenly.

#### Jack

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #2 on: July 05, 2016, 09:53:18 AM »
Pay as much as you can afford on the highest-rate loan and the minimum on all the others.

#### frugalnacho

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #3 on: July 05, 2016, 11:26:24 AM »
I don't really understand the confusion.  Each loan will have a minimum required payment, so pay that for each loan.  Then use whatever money you have left over for the debt with the highest interest rate.

#### thingamabobs

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #4 on: July 05, 2016, 02:16:38 PM »
They are basically the same given one has higher balance and lower interest rate and the other exact opposite. Just split it \$500 each and you'll have them both paid off by 2020. Of course if you can throw more money at them as time goes on, you can pay them off faster.

#### onlykelsey

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #5 on: July 05, 2016, 02:24:24 PM »
I don't really understand the confusion.  Each loan will have a minimum required payment, so pay that for each loan.  Then use whatever money you have left over for the debt with the highest interest rate.

Agreed.  And I actually (respectfully) disagree with the advice below from thingamabobs.  The sooner you can get one 100% paid off, the better.  If something goes wrong, I'd rather have one creditor coming after me for 10K than two for 5K each.

#### FIPurpose

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #6 on: July 05, 2016, 02:49:49 PM »
I wouldn't call a .74% difference in loan rates negligible. On \$20k that's an additional \$150 in interest per year. Pay off the higher interest rate.

#### thingamabobs

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #7 on: July 06, 2016, 10:32:33 AM »
I don't really understand the confusion.  Each loan will have a minimum required payment, so pay that for each loan.  Then use whatever money you have left over for the debt with the highest interest rate.

Agreed.  And I actually (respectfully) disagree with the advice below from thingamabobs.  The sooner you can get one 100% paid off, the better.  If something goes wrong, I'd rather have one creditor coming after me for 10K than two for 5K each.

I can see that, but if they are fed student loans then they can apply for hardship regardless of number of loans.

So I did some calculations using a interest calculator. OP stated that they had \$1000 to apply toward loans and I applied \$500 to each.

5.16% loan total interest \$2327.64
5.9% loan total interest \$2493.00

Calculators estimate payments end  in 2020.

So that's a total difference over the life of the loans of \$165.36 over 4 years!! Who knows how long the OP has been trying to figure this out. I understand about saving and cutting costs whenever possible but I also believe in not overcomplicating things.

ETA: typo

#### frugalnacho

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #8 on: July 06, 2016, 10:46:52 AM »
I don't really understand the confusion.  Each loan will have a minimum required payment, so pay that for each loan.  Then use whatever money you have left over for the debt with the highest interest rate.

Agreed.  And I actually (respectfully) disagree with the advice below from thingamabobs.  The sooner you can get one 100% paid off, the better.  If something goes wrong, I'd rather have one creditor coming after me for 10K than two for 5K each.

I can see that, but if they are fed student loans then they can apply for hardship regardless of number of loans.

So I did some calculations using a interest calculator. OP stated that they had \$1000 to apply toward loans and I applied \$500 to each.

5.16% loan total interest \$2327.64
5.9% loan total interest \$2493.00

Calculators estimate payments end  in 2020.

So that's a total difference over the life of the loans of \$165.36 over 4 years!! Who knows how long the OP has been trying to figure this out. I understand about saving and cutting costs whenever possible but I also believe in not overcomplicating things.

ETA: typo

I don't understand how any of this information is useful.  What good is calculating the interest paid over the life of two different loans, with different balances, and different interest rates with an arbitrary scenario of splitting \$1k/mo between the loans?  The interest rate already tells you the most efficient way to pay it down without doing any math at all.

#### thingamabobs

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #9 on: July 06, 2016, 11:13:14 AM »
How is it not useful?? Isn't the whole point of recommending paying down the higher interest rate loan first is to decrease the amount of interest paid overall?? So how does OP, who is just starting out and learning, know how much they are going to be saving if they don't know how much they would have been paying. I get what you're saying, "duh! it's simple!" but obviously not to OP since they posted the question.

The reason I did the math is to show OP and others who are in similar situations that since they couldn't figure out how much to pay for both, an even split would not be that horrible in the long run. And hopefully save others some time in the future that they can use to be more productive in other ways.

BTW: If OP pays minimum (not sure how long your loan term is, I assumed 10 years) on the lower interest rate and puts the rest of their \$1000 towards the higher interest loan the total interest comes to approx \$4900. 50/50 split the total interest is 4820.64

#### frugalnacho

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #10 on: July 06, 2016, 12:24:44 PM »
How is it not useful?? Isn't the whole point of recommending paying down the higher interest rate loan first is to decrease the amount of interest paid overall?? So how does OP, who is just starting out and learning, know how much they are going to be saving if they don't know how much they would have been paying. I get what you're saying, "duh! it's simple!" but obviously not to OP since they posted the question.

The reason I did the math is to show OP and others who are in similar situations that since they couldn't figure out how much to pay for both, an even split would not be that horrible in the long run. And hopefully save others some time in the future that they can use to be more productive in other ways.

BTW: If OP pays minimum (not sure how long your loan term is, I assumed 10 years) on the lower interest rate and puts the rest of their \$1000 towards the higher interest loan the total interest comes to approx \$4900. 50/50 split the total interest is 4820.64

The question wasn't to calculate out how much interest would be paid in various options, it was just "how much should go towards each loan", with the reasoning that they are trying to optimize their finances.  In that situation the answer is that 100% of available excess funds should go towards the higher interest rate.  I don't even have to do the math to know that the most optimal solution is paying the highest interest rate down the fastest.

And speaking of the math:

loan 1 is \$21,501 @ 5.16%.  Assume 10 years gives monthly payment of \$229.74
loan 2 is \$20,653 @ 5.9%.  Assume 10 years gives monthly payment of \$228.25

Option 1 is to split the payment between both, and pay an additional \$271.01 on each loan. Last payment is done on payment #47 with an additional \$33.39 left over that payment.  Total interest paid is \$4813.12

Option 2 is to pay loan 2 off fastest.  Last payment is done on payment #47 with an additional \$162.55 left over that payment.  Total interest paid is \$4683.45.

An overall difference of about \$130.

The exact length of loan, and the exact amount of money saved is somewhat irrelevant though.  The main take away is that if you toss everything into a spreadsheet, EVERYTHING will cancel and the only important piece of information is the interest rate.  Paying off the highest interest rate as fast as possible is the most optimal solution and will save you the most money.  Any other scenario is financially sub-optimal by definition.

#### thingamabobs

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #11 on: July 06, 2016, 01:21:47 PM »
Again, I know that most of the people on the forum don't need to do the math but it is still helpful to show why you recommend doing things a certain way. I think it helps educate people  and therefore I don't think it's unnecessary. For a lot of people percentages are very abstract until you show them the numbers. Hence why a lot of people buy cars with "affordable" monthly payments not realizing how much they will be paying in the long run. Which is why I feel knowing how much total interest one would be paying using one method versus another is important.

oops, I was wrong on the total interest amounts. Of course there would be savings by paying off the higher interest loan first. My mistake. But again, the amount saved... Yes, paying off the higher interest rate loan ASAP is the optimal solution but not necessarily the right one for everyone which is why I gave the example that I did.

#### Jack

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #12 on: July 06, 2016, 02:03:35 PM »
oops, I was wrong on the total interest amounts. Of course there would be savings by paying off the higher interest loan first. My mistake. But again, the amount saved... Yes, paying off the higher interest rate loan ASAP is the optimal solution but not necessarily the right one for everyone which is why I gave the example that I did.

First of all, of course the [mathematically-]optimal solution is necessarily the right one for everyone! ; )

Second, even if it isn't, paying equal amounts is still not the best plan either. If you prefer a touchy-feely emotional solution to the cold hard facts of math, then you should be doing a Dave Ramsey-style snowball (paying the minimum on everything except the loan with the lowest outstanding balance, so that you can get individual loans to \$0 ASAP for that hit of paid-off satisfaction).

Lazily making equal payments to loans without regard to interest rate or balance owed may not be the most pessimal way of paying them off, but it's certainly solidly in the realm of 'mediocre', and this is not a forum for lazy mediocrity!

#### MDM

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #13 on: July 06, 2016, 02:35:54 PM »
I currently have two student loans with different interest rates and, of all the loan calculators out there, I couldn't find one to answer this question: How should I divide my payment between a 21,501.00 loan at 5.16% interest and a 20,653 loan at 5.9% interest? For example, if I have \$1,000.00 to put towards loans each month, how much should go towards each loan?
As already stated: pay the minimum required (call that "\$X") on the 5.16% one, and (\$1000 - \$X) on the 5.9% one.

See http://www.vertex42.com/Calculators/debt-reduction-calculator.html for a spreadsheet you can download that will allow you to answer this question for yourself.  Good luck!

#### FIPurpose

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #14 on: July 06, 2016, 03:41:31 PM »
There is one instance where not paying the highest loan rate makes sense, but this is not one of those examples. I would only think it better to pay down lower interest rate loans if you have a lot of small low rate loans and one large high interest loan, and even then only really if you are worried about short-term cash-flow issues.

Example:

Loan 1: \$10,000 @ 4.5% 60 month
Loan 2: \$10,000 @ 3% 60 month
Loan 3: \$30,000 @ 8% 60 month

This comes out to a required cash-flow of about \$975 per month. If the person feels that something soon may interrupt being able to pay that much, it may be in their best interest to pay the lower rates first to reduce cash-flow needs. By paying off Loans 1 and 2, the person can reduce minimum necessary cash-flow by \$365/month. Of course if there is no danger of losing income, then paying the higher interest rate is still mathematically better.

But like I said this is not that situation. OP's higher interest loan is also the smaller of the two. There is no cash-flow advantage in paying off any extra to the lower-interest loan, and it would actually be worse for the OP to pay off both at the same time rather than one or the other.

#### frugalnacho

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #15 on: July 07, 2016, 11:10:20 AM »
There is one instance where not paying the highest loan rate makes sense, but this is not one of those examples. I would only think it better to pay down lower interest rate loans if you have a lot of small low rate loans and one large high interest loan, and even then only really if you are worried about short-term cash-flow issues.

Example:

Loan 1: \$10,000 @ 4.5% 60 month
Loan 2: \$10,000 @ 3% 60 month
Loan 3: \$30,000 @ 8% 60 month

This comes out to a required cash-flow of about \$975 per month. If the person feels that something soon may interrupt being able to pay that much, it may be in their best interest to pay the lower rates first to reduce cash-flow needs. By paying off Loans 1 and 2, the person can reduce minimum necessary cash-flow by \$365/month. Of course if there is no danger of losing income, then paying the higher interest rate is still mathematically better.

But like I said this is not that situation. OP's higher interest loan is also the smaller of the two. There is no cash-flow advantage in paying off any extra to the lower-interest loan, and it would actually be worse for the OP to pay off both at the same time rather than one or the other.

I don't think prepaying those loans would reduce the minimum required payments, at least none of the loans I have ever had worked that way.  The term was set, and a payment schedule was produced, and any additional payments would pay off the balance of the loan which would change how much of the future payments were divided between interest and principle, but the payment was still the same as when the loan originated.

#### Jack

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #16 on: July 07, 2016, 11:17:02 AM »
I don't think prepaying those loans would reduce the minimum required payments

Sure it would, when the loan balance hit \$0! FIPurpose was just explaining the 'snowball' method without actually naming it.

#### FIPurpose

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##### Re: Calculating ideal payments for student loans with different interest rates
« Reply #17 on: July 07, 2016, 03:01:06 PM »
There is one instance where not paying the highest loan rate makes sense, but this is not one of those examples. I would only think it better to pay down lower interest rate loans if you have a lot of small low rate loans and one large high interest loan, and even then only really if you are worried about short-term cash-flow issues.

Example:

Loan 1: \$10,000 @ 4.5% 60 month
Loan 2: \$10,000 @ 3% 60 month
Loan 3: \$30,000 @ 8% 60 month

This comes out to a required cash-flow of about \$975 per month. If the person feels that something soon may interrupt being able to pay that much, it may be in their best interest to pay the lower rates first to reduce cash-flow needs. By paying off Loans 1 and 2, the person can reduce minimum necessary cash-flow by \$365/month. Of course if there is no danger of losing income, then paying the higher interest rate is still mathematically better.

But like I said this is not that situation. OP's higher interest loan is also the smaller of the two. There is no cash-flow advantage in paying off any extra to the lower-interest loan, and it would actually be worse for the OP to pay off both at the same time rather than one or the other.

I don't think prepaying those loans would reduce the minimum required payments, at least none of the loans I have ever had worked that way.  The term was set, and a payment schedule was produced, and any additional payments would pay off the balance of the loan which would change how much of the future payments were divided between interest and principle, but the payment was still the same as when the loan originated.

Exactly, in the example, paying off the lower interest loans first would reduce the minimum payments faster than paying off the larger, higher interest loan first. If you have \$20,000 that you could put toward the loans, the two options you have are either to pay the highest interest or the lower balances:

1. Pay highest interest:
Amount owed: \$30k
Average Interest: 5.1%
Minimum payment: \$975

2. Pay off the 2 lower interest loans
Amount owed: \$30k
Average Interest: 8%
Minimum payment: \$608

That is the trade off I was trying to describe.