quick finance question - paying down loan early

[Special K]

I need to do a quick sanity check here - let's say I have a loan with a fixed interest rate, and I have some extra money each month that I can either use to pay down the loan (no early repayment penalty), or invest in something else, such as an online savings account. Let's say the interest rate of the loan equals the interest rate of the investment.

Over equal periods of time, should the amount saved in interest by "investing" the extra money in the loan exactly equal the interest I would make by instead putting the money in the investment?

EDIT: assume the interest in the savings account (or whatever) is compounded monthly, just to simplify things. I realize most of the online accounts compound daily.

 

[FoBoT]

as long as the interest earned is compounded at the same rate/frequency as the interest charged by the loan is accessed

then yes, flip a coin. or if you are anti-debt, pay off the loan

i would pay off the loan

 

[msparish]

It will be the same, but you'll have to pay taxes on any interest you earn. Therefore, unless you are getting tax breaks on the loan interest (e.g. mortgage), you will save more money by paying down the loan early. However, you can earn higher rates of return from things other than an online savings account, and if you pay down the loan early you lose liquidity.

 

[newmachineoverlord]

<div class="FTQUOTE"><begin quote>Originally posted by: msparish
It will be the same, but you'll have to pay taxes on any interest you earn. Therefore, unless you are getting tax breaks on the loan interest (e.g. mortgage), you will save more money by paying down the loan early. However, you can earn higher rates of return from things other than an online savings account, and if you pay down the loan early you lose liquidity.</end quote></div>

All true. The other factor is that by paying down the loan you are more rapidly improving your credit score, which might qualify you for an even lower interest loan to convert the rest of the debt to a lower interest rate. If your total minimum payments on all debts amount to less than 10percent of your income then this isn't a big factor, but it's the only thing msparish left out. Paying off the loan also requires less effort on your part than finding something else that earns a higher rate of return.

edit: extraneous comma removed

 

[Kelemvor]

They say that just making one extra payment per year on a 30 year mortgage can let you pay it off in like half the time. I'd go that route.

 

[PingSpike]

Originally posted by: Kelemvor
They say that just making one extra payment per year on a 30 year mortgage can let you pay it off in like half the time. I'd go that route.

Its more like 6 years.

 

[Special K]

Originally posted by: msparish
It will be the same, but you'll have to pay taxes on any interest you earn. Therefore, unless you are getting tax breaks on the loan interest (e.g. mortgage), you will save more money by paying down the loan early. However, you can earn higher rates of return from things other than an online savings account, and if you pay down the loan early you lose liquidity.

Does the initial amount of the loan affect whether or not it's a better deal to pay it off early rather than investing, all other things being equal?

That is, if the loan has a fixed interest rate of 5%, the savings account pays 5%, would having a $75,000 vs. a $50,000 loan make any difference in the result, ignoring any taxes or tax breaks?

 

[mugs]

Originally posted by: Special K
<div class="FTQUOTE"><begin quote>Originally posted by: msparish
It will be the same, but you'll have to pay taxes on any interest you earn. Therefore, unless you are getting tax breaks on the loan interest (e.g. mortgage), you will save more money by paying down the loan early. However, you can earn higher rates of return from things other than an online savings account, and if you pay down the loan early you lose liquidity.</end quote></div>

Does the initial amount of the loan affect whether or not it's a better deal to pay it off early rather than investing, all other things being equal?

That is, if the loan has a fixed interest rate of 5%, the savings account pays 5%, would having a $75,000 vs. a $50,000 loan make any difference in the result, ignoring any taxes or tax breaks?

No, because paying down the loan only saves you interest on the amount that you pay off, which would be equal to the amount you put in savings.

 

[bsobel]

Originally posted by: Special K
<div class="FTQUOTE"><begin quote>Originally posted by: msparish
It will be the same, but you'll have to pay taxes on any interest you earn. Therefore, unless you are getting tax breaks on the loan interest (e.g. mortgage), you will save more money by paying down the loan early. However, you can earn higher rates of return from things other than an online savings account, and if you pay down the loan early you lose liquidity.</end quote></div>

Does the initial amount of the loan affect whether or not it's a better deal to pay it off early rather than investing, all other things being equal?

That is, if the loan has a fixed interest rate of 5%, the savings account pays 5%, would having a $75,000 vs. a $50,000 loan make any difference in the result, ignoring any taxes or tax breaks?

No, the math is size invariant...
Bill

 

[theeedude]

If you are making SAME interest rate on investment as your loan fixed interest rate, DO NOT PAY OFF THE LOAN.
If your rate of return on investment goes down, you can always pay off the loan later. But if your rate of return on investment goes up, you will not have an option of borrowing at the same interest rate you have now. It's called liquidity preference.

 

[Special K]

Alright, I'm messing around in Excel right now and something isn't consistent. Here is the test scenario:

$100,000 loan at 7.5% fixed APR, 10 year term

I am assuming an extra $500/month to either pay off the loan, or invest. To keep the math easier, I assume the rate of return on the investment is also 7.5%. Probably not realistic, but it made the comparison easier.

So if I do nothing, I end up paying $100,000 for the principle, and $42,442 for the interest. I verified my spreadsheet against a calculator on bankrate.com, so I know this part is correct. The total amount paid is $142,442 (obviously).

Now if I pay an extra $500/month on the loan, I end up paying it off in 75 months, and only pay $25,309.07 in interest. I again verified my calculations against the bankrate calculator, and it matches up. So you "save" ($42,442 - $25309.02 = $17,132.93) in interest. The total amount paid is $125,309.07.


Now if I put that $500 in an investment earning 7.5% APR and compounded monthly, I would have invested $37,000 in it over the same timeframe as if I had paid the loan off early. At the end of that time, it would have grown to $47,153.28. So I made ($47,153.28 - $37,000 = $10,153.28) in interest, but have to pay $42,442 in interest. The net amount is therefore $100,000 + $42,442 (interest paid on loan) - $10,153.28 (interest earned from investment) = $132,228.72.

Now why do I end up paying more when I put the money in the investment? Shouldn't it come out exactly equal to the total amount paid when I pay off the loan early? I know I'm ignoring taxes and stuff, but shouldn't the numbers come out equal in the above scenario?

 

[sdifox]

Originally posted by: Special K
Alright, I'm messing around in Excel right now and something isn't consistent. Here is the test scenario:

$100,000 loan at 7.5% fixed APR, 10 year term

I am assuming an extra $500/month to either pay off the loan, or invest. To keep the math easier, I assume the rate of return on the investment is also 7.5%. Probably not realistic, but it made the comparison easier.

So if I do nothing, I end up paying $100,000 for the principle, and $42,442 for the interest. I verified my spreadsheet against a calculator on bankrate.com, so I know this part is correct. The total amount paid is $142,442 (obviously).

Now if I pay an extra $500/month on the loan, I end up paying it off in 75 months, and only pay $25,309.07 in interest. I again verified my calculations against the bankrate calculator, and it matches up. So you "save" ($42,442 - $25309.02 = $17,132.93) in interest. The total amount paid is $125,309.07.


Now if I put that $500 in an investment earning 7.5% APR and compounded monthly, I would have invested $37,000 in it over the same timeframe as if I had paid the loan off early. At the end of that time, it would have grown to $47,153.28. So I made ($47,153.28 - $37,000 = $10,153.28) in interest, but have to pay $42,442 in interest. The net amount is therefore $100,000 + $42,442 (interest paid on loan) - $10,153.28 (interest earned from investment) = $132,228.72.

Now why do I end up paying more when I put the money in the investment? Shouldn't it come out exactly equal to the total amount paid when I pay off the loan early? I know I'm ignoring taxes and stuff, but shouldn't the numbers come out equal in the above scenario?

Lol, the principals are different. Mortgage principal start out high and is reduced over time, your investment start with low principal then build up over time. Because it is compound interest, you pay more. I never understand the people who like to invest rather than pay down debt.

 

[msparish]

Originally posted by: Special K
Alright, I'm messing around in Excel right now and something isn't consistent. Here is the test scenario:

$100,000 loan at 7.5% fixed APR, 10 year term

I am assuming an extra $500/month to either pay off the loan, or invest. To keep the math easier, I assume the rate of return on the investment is also 7.5%. Probably not realistic, but it made the comparison easier.

So if I do nothing, I end up paying $100,000 for the principle, and $42,442 for the interest. I verified my spreadsheet against a calculator on bankrate.com, so I know this part is correct. The total amount paid is $142,442 (obviously).

Now if I pay an extra $500/month on the loan, I end up paying it off in 75 months, and only pay $25,309.07 in interest. I again verified my calculations against the bankrate calculator, and it matches up. So you "save" ($42,442 - $25309.02 = $17,132.93) in interest. The total amount paid is $125,309.07.


Now if I put that $500 in an investment earning 7.5% APR and compounded monthly, I would have invested $37,000 in it over the same timeframe as if I had paid the loan off early. At the end of that time, it would have grown to $47,153.28. So I made ($47,153.28 - $37,000 = $10,153.28) in interest, but have to pay $42,442 in interest. The net amount is therefore $100,000 + $42,442 (interest paid on loan) - $10,153.28 (interest earned from investment) = $132,228.72.

Now why do I end up paying more when I put the money in the investment? Shouldn't it come out exactly equal to the total amount paid when I pay off the loan early? I know I'm ignoring taxes and stuff, but shouldn't the numbers come out equal in the above scenario?

You aren't looking at it correctly. You haven't paid the entire $42,442 in interest until the entire 10 year period is over. Assuming your calculations are correct the amount in savings should be able to pay off the remaining amount of the loan at month 75.

If you want to compare the total money saved, you need to extend the amount of savings over the entire 10 years for both loans.

 

[patentman]

I hate being in debt, so I always try to pay down all my loans as fast as possible. Obviously a house takes a while, but I still tack on a couple hundred extra to my mortgage payment every month. 1 extra payment a year on a 30 year fixed takes 9-12 years off the loan.

 

[jadinolf]

Originally posted by: FoBoT
as long as the interest earned is compounded at the same rate/frequency as the interest charged by the loan is accessed

then yes, flip a coin. or if you are anti-debt, pay off the loan

i would pay off the loan

:thumbsup:

 

[WingZero94]

Pay off the loan. Loan = Guaranteed. You'll always owe the money.

Investment = Not Guaranteed - You can lose the money.

 

[theeedude]

Originally posted by: WingZero94
Pay off the loan. Loan = Guaranteed. You'll always owe the money.

Investment = Not Guaranteed - You can lose the money.

Ever hear of fixed income investments?

 

[FP]

Originally posted by: WingZero94
Pay off the loan. Loan = Guaranteed. You'll always owe the money.

Investment = Not Guaranteed - You can lose the money.

Ever hear of leverage?

 

[Special K]

Originally posted by: sdifox
Lol, the principals are different. Mortgage principal start out high and is reduced over time, your investment start with low principal then build up over time. Because it is compound interest, you pay more. I never understand the people who like to invest rather than pay down debt.

But two other posters above said the principle amount didn't matter:

Originally posted by: mugs
No, because paying down the loan only saves you interest on the amount that you pay off, which would be equal to the amount you put in savings.

and

Originally posted by: bsobel
No, the math is size invariant...
Bill

 

[beguile]

Originally posted by: binister
<div class="FTQUOTE"><begin quote>Originally posted by: WingZero94
Pay off the loan. Loan = Guaranteed. You'll always owe the money.

Investment = Not Guaranteed - You can lose the money.</end quote></div>

Ever hear of leverage?

You should explain the concept to them. I use to think like the OP but I would drag my loan as much as possible.

 

[FP]

Originally posted by: Special K
Alright, I'm messing around in Excel right now and something isn't consistent. Here is the test scenario:

$100,000 loan at 7.5% fixed APR, 10 year term

I am assuming an extra $500/month to either pay off the loan, or invest. To keep the math easier, I assume the rate of return on the investment is also 7.5%. Probably not realistic, but it made the comparison easier.

So if I do nothing, I end up paying $100,000 for the principle, and $42,442 for the interest. I verified my spreadsheet against a calculator on bankrate.com, so I know this part is correct. The total amount paid is $142,442 (obviously).

Now if I pay an extra $500/month on the loan, I end up paying it off in 75 months, and only pay $25,309.07 in interest. I again verified my calculations against the bankrate calculator, and it matches up. So you "save" ($42,442 - $25309.02 = $17,132.93) in interest. The total amount paid is $125,309.07.


Now if I put that $500 in an investment earning 7.5% APR and compounded monthly, I would have invested $37,000 in it over the same timeframe as if I had paid the loan off early. At the end of that time, it would have grown to $47,153.28. So I made ($47,153.28 - $37,000 = $10,153.28) in interest, but have to pay $42,442 in interest. The net amount is therefore $100,000 + $42,442 (interest paid on loan) - $10,153.28 (interest earned from investment) = $132,228.72.

Now why do I end up paying more when I put the money in the investment? Shouldn't it come out exactly equal to the total amount paid when I pay off the loan early? I know I'm ignoring taxes and stuff, but shouldn't the numbers come out equal in the above scenario?

You don't have to pay $42,442 in interest because that was the amount of interest if the loan was taken to term (10 years).

Look at the amount of interest accrued at 75 months. That is the amount you would have to pay. Your investment should return that amount.

 

[FP]

Ok I did the calculation for ya...

Scenario #1: Do nothing... You end up paying $42,442.12 in interest over the 10 years.

Scenario #2: Pay down the loan... The loan is paid off in 75 months and you have paid $25,309.07 in interest.

Scenario #3: Invest the money... At 75 months you pay off the loan in full. You have ~$47,000 in your investment account of which ~$10,000 is accrued interest. Your loan balance is $46,436.02 which is just about what you have in your investment account so you are able pay off the loan in full. You have paid more in interest on the loan but you have made up that difference in your investments so it is a wash.

Everything doesn't add up perfectly because of rounding errors and other minor mistakes but you get the general idea.

Personally I would always go with scenario #3 because you have more options.

 

[Savarak]

http://www.fool.com/foolu/askf...001/askfoolu010307.htm has a really good article that confirms many things...

 

[Savij]

Split the difference and work on the investments and work on the loans?

 

[FP]

If you are good with money and know you won't spend it then there is no reason to pay the loan down vs. investing the money.

Paying the loan down only makes the bank sleep better at night. You should use that money to diversify your portfolio and reduce your risk.