# Complete Opposite Calculations and Opinions - Using Loan to Invest - Paying Monthly Installments with Monthly Income

I managed to discuss Using Loan to Invest - Paying Monthly Installments with Monthly Income with a friend and his answer underneath is completely opposite from the current answers. Please understand I'm quoting my friend – He can be wrong and caustic. Please don't be offended.

Question: Suppose a bank gives – ● Loan = 8,266.67 USD, ● Months = 24,
● Monthly interest rate = 0.27%, so total loan interest paid = \$0.027*8266.67*24 = \$535.68.
● The loan must be repaid in monthly installments. Excel's PMT(.0027, 24, -8266.67, 0) = \$356.19
● My monthly salary = I. So I > \$356.19
● Tax rate = 0 ≤ T < 1. Then (1 – T)(Breakeven Amount) = After-tax Capital gain.
I pay off the monthly loan installments only with his monthly employment income I. To maximize profit, assume I buy stocks in the 1st month and hold them until the 24th month.

My friend says —

You have \$8266.67 from the loan to invest, and will breakeven if the stocks return \$535.68. This is over 2 years, so we have two choices : simple or compound return. We also need to know if they want total return or annualized return, but I think we're safe to assume simple return, which is 535.68/8266.67 = 6.48%. This is the cost of money. Actually, that's 3.24% annual average, we calculated total cost as a total minimum (break even) return. So the market rate of return — say 10% per year — should have been compared to 3.24% per year, and it's even MORE profitable as long as the market doesn't tank and stay down for the whole two years.

In finance, the term "return" ALWAYS refers to the percentage OVER the investment that is earned, because we assume that unless you end up with a negative return you will get the investment back. The majority of each payment is principal, which is the same money you invested, so it would not be part of the return.

THEAO's answer and Chris Degnen's are incorrect because it bases the needed returns on the pay. This is wrong because the payments include the principal (are, in fact, mostly principal). Borrowed money costs interest and only interest.

If you and I are out to lunch and I forgot to stop at the ATM and you loan me \$20, that's still your \$20 that I invested in my lunch. Then I give you back your \$20 and if you didn't charge me interest it cost me nothing: I got a \$20 lunch, I just paid you back for it later. The principal is just like the \$20 you loaned me at lunch: it's the same money he invested, and if your return is 0% (like when I paid you back for lunch) you STILL get the principal back. It's a common error, because the concept of borrowed money not being a cost is not exactly intuitive.

If the return on the investment is 3.24% per year or 6.48% for the entire two years (allowing that one year can be low as long as the other is high enough to fix the average) he breaks even based on the cost of the loan. Any return over 3.24% per year average for the two years (less any taxes) is profit.

Cosmic difference! In the previous question, many said it's bad using this loan to invest in stocks. But my friend seems to say this is profitable for laymen like me — the required rate of return to breakeven with the cost of loan is 3.24% annually. So who's right and wrong? Where are the common grounds and mistakes?

• What does your friend say happens if the investment loses money? Does your friend do this himself? What is your friend's interest in giving this advice? The most important question of all, does this make clear and obvious sense to you? – MrChrister Nov 12 '13 at 14:52
• Why the close votes? The question is asking about something somebody stated as fact, and I think the answer will prove it is wrong. The question explains the position very well, and it will improve the Internet to provide great counterpoints to the strategy being asked about. – MrChrister Nov 12 '13 at 15:02
• @MrChrister: Thanks so much. My friend did it himself but I doubted him so I thought to ask you experts here. I'm super glad I did. I still don't understand this so I posted another question just on the calculations. I'll think more about this and bug my "friend" ;) more. – user11761 Nov 13 '13 at 7:35
• @MrChrister - the underlying question is fine. The way the OP has quoted a friend who both disagrees and goes off on tangents makes this a fast TLDR situation. We now have 3 questions, each asking a minor variation of what, in my opinion, could be a single, succinct, question. (I'm making this comment to you even though I didn't not vote to close this one, only the third in this series. – JTP - Apologise to Monica Nov 13 '13 at 15:38
• @dresserse - as I commented to MrC, your question here goes on and on, and the intent is lost. Simple problems shouldn't require this much background. – JTP - Apologise to Monica Nov 14 '13 at 11:14

The advice you were given in the other question was don't do it. The math is not the issue. The interest structure is not the issue. But there is a significant chance that you could lose money on the deal. If you invested your money in a NASDAQ heavy position in January 2000, you are still waiting to break even in November of 2013; Invest in almost anything in August 2001 and you will be down for a long time. Invest just before the housing collapse in 2007 and only now returning back to where you were.

If you take money on a monthly basis and invest it you will be better off.

If want to get the loan; then set up a stream of money into a bank account to make sure that when payments are due you have the cash to do so. When the two years are up you will have cash to repay the loan, and no need to sell the investments. Also if you are a bad judge of investments you won't have a problem repaying the loan.

Using a loan to purchase stock reduces your gains and increases your losses. Use the power of Dollar cost averaging by making periodic purchases.

• +1 for an excellent answer that was much less long-winded than mine. – THEAO Nov 12 '13 at 11:46

Sorry in advance, but this will be long.

Also, it sounds like your friend is a tool. I hope this "friend" is not also your financial advisor... they would be encouraging you to make a very poor investment decision. They also don't know how to do financial math.

For what it's worth, I am not wrong. I have correctly answered a set of changing questions as you have asked them... Your friend is answering based on a third, completely different investment model, which you proposed in the edit to your last post. If that's what you meant all along, then you should have been more clear in the questions you were asking.

Please let me layout the following:

• How the previous questions//investment proposals were built

• How to analyze this current proposal

• What your other option is

• Why the other option is best in a 'real world' market

The First Question My understanding of the initial proposal was to take out a \$10,000 loan, invest the proceeds, and expect to not have any money of your own tied up in this. Because that OP did not specify that this is an interest-only loan (you still haven't in any of your questions), the bank will require you to make payments back to them each month that include principal and interest.

Your "friend" is talking about the total interest paid being the only cost of a loan. While that is (almost) true, regardless of what your friend says, significantly more cash is involved in making sure that all the payments are made on time---unless you set up an interest-only loan. But with the set up laid out in this post, and with the assumptions I specified there, the principal payments must be included because the borrower has to pay back the bank and isn't not tying up any of their own money.

In that case, my initial analysis is correct--your breakeven is in the low teens for an annual required return.

The Second Proposal Your second proposal... before any edits... refined things a little bit, to try to capture the any possible returns by not selling something. As I indicated there, (with what was an exaggerating assumption), the lack of clarity makes for an outlandish required return.

The Second Proposal...with edits, or the one proposed above I will get to the one proposed above in a second, but first let me highlight a few problems with your friend's analysis.

• Simple interest: the only place (in the US at least) that will lend with simple interest is student loans. Any loan that you actually take out will be compound interest.

• Not an interest only loan: your "friend" is not calculating interest correctly. Since this isn't an interest-only loan, the principal balance will reduce every time you make a payment, by ~\$320-\$340 each month. This substantially reduces the total interest paid, to \$272.79 over the total 24 months.

• "Returns": I don't know what country, or what business your friend works in, but "returns" are a very ambiguous concept. Investopedia defines returns as gains or losses. (I wish I could inhabit the lala land that your friend lives in when returns are always positive). TheFreeDictionary.com defines a return for finance as "The change in the value of a portfolio over an evaluation period, including any distributions made from the portfolio during that period."

When you have not made it clear that any other money is being used in this investment plan (as was the case in scheme #1 and scheme #2a,) the loan still has to be paid. So, clearly the principal must be included in the return calculations.

How to evaluate this proposed investment scheme

Key dimensions:

• Loan (\$8,000 ... 24 months ... 0.27% monthly rate... monthly compounding... no loan origination fees)

• Monthly payment (PMT in Excel yields \$344.70).

• Investment capital (starting = \$8,000)

• Monthly Return (Investment yields... we hope it's positive!)

• Your monthly contribution from your salary

• Taxes = 10%.

• Transaction Fees = \$20

Go and lookup how to build an amortization table for a loan in Excel. Your life will be infinitely better for it.

Now, you get this loan set up and invested into something... (it costs \$20 to buy the assets).

So you've got \$7980 chugging away earning interest. I calculate that your break even, with you paying in \$344.70 of your own money each month is 1.81% annually, or 3.42% over the 24 month life of this scheme. That is using monthly compound interest for the payments, because that's what the real world would use, and using monthly compounding of the investments' returns.

Your total interest expense would be \$272.79.

This seems feasible. But let's talk about what your other option is, given that you're ready to spend \$344.70 each month on an investment.

I understand the appeal of getting \$8,000... right away... to invest in something. But the risk behind this is that if the market goes down (and markets do) you're stuck paying a fixed amount for your loan that is now worth less money.

Your other option is to take your \$344.70, and invest it step-by-step. (You would want to skip a month or two buying assets in the market, so that you can lessen transaction costs).

This has two advantages: (1) you save yourself \$272 in interest. (2) When the market goes down, you still win.

With this strategy, you still win when the market goes down because of what is commonly called "dollar cost averaging". When the market is up, your investments are also up. When the market goes down, your previous investments decrease in value but you can invest new money at the lower rates.

Why the step-by-step, invest your own money strategy is better

At low rates (when you're looking for your break-even), the step-by-step model outperforms the loan. At higher rates of return (~4% + per year), you get the benefit of having the borrowed money earning more gains.

In fact, for every continuous (meaning set... not changing month-to-month) interest rate that you can dream up that is greater than about 4% per year, the borrowed money earns more.

At 10% per year, the borrowed money will earn about \$500 more over the 2 years than your step by step investment would.

BUT

I recognize that you might feel like the market will always go up. That's what everyone thinks. And that's alright.

But have one really bad month, or a couple of just-not-great-months, and your fixed 'loan' portfolio will underperform. Have a few really bad months, and your portfolio could be substantially reduced in value... but you would still be paying the same amount for it each month.

And if that happened (say your assets declined -3% in 3 of the 24 months...) You'd be losing money relative to the step-by-step portfolio.

• Thanks a lot. Really appreciate your help. Please don't be offended. I was just quoting him directly. I'll tell my friend off now - you're more of a friend than him. – user11761 Nov 13 '13 at 7:37
• I also tried calculating with Excel. I am stuck so posted another question just on calculating. Really appreciate your answer again there if I haven't bugged you enough already. – user11761 Nov 13 '13 at 7:38