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I am facing a dilemma.

I have 82k in cash and I have an 82k remaining mortgage to pay off. I can either continue the mortgage and invest my 82k cash into an investment vehicle (FD/CD) @ 7%, or just use my 82k cash to pay off my 82k remaining mortgage completely and end it.

My monthly installment for the mortgage is $905 which is made up of $710 going towards capital reduction and $195 going towards interest for the loan.

I am very confused because both my calculations end up in two different conclusions:

  • A: Since 7% of 82k = $5740, my yearly income would be $5740 if I
    continued paying $905 per month and invested the 82k. Also, My yearly expense would be $905 x 12 = $10,860 due to installment payments. So, on net, my yearly cashflow = $5740 - $10,860 = -$5120, compared to 0 if I paid off my mortgage right now. Clearly, paying up lump sum is better.
  • B: Another way to look at it. My interest that I would get from the investment vehicle is 7%. The mortgage interest to the bank is 2.84%, which I calculated approximately as (($195x12)/82k)x100, which represents the annual interest portion of my installment payments as a percentage of mortgage remaining. Hence, clearly, continuing the loan while investing the 82k @ 7% is better (7% > 2.84%).
  • C: ? Are there any other ways of looking at this situation?

Could anyone shed some light on this? Am I calculating anything wrong? I would appreciate any help greatly.

  • 1
    Your analysis does not factor in taxes. Money to pay a mortgage is typically from after-tax funds (e.g. a salary) while earnings on a deposit are typically taxable interest payments. So comparing 2.84% to 7% might not be an apples-to-apples comparison. Could you provide some information about taxation for your country? – Chris W. Rea Jun 26 '18 at 12:00
  • Note it sounds like you are assuming the 7% return is guaranteed, and I'm guessing it's not. – TTT Jun 26 '18 at 14:00
  • Where are you getting a secure/guaranteed investment with a 7% return? In the US, that's around the general average for the stock market, but I've never seen a CD anywhere near that – kchason Jun 26 '18 at 17:25
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Your calculations are showing you two sides of the same coin.

Calculation A is showing you negative cash flow because the mortgage is essentially requiring you to pay into the equity of your home. The entire mortgage payment is not an expense - anything not going to interest is going to your home equity, which does not decrease your net worth.

Which is what calculation B shows you - that your total net worth will grow more with a 7% return vs a 2% return.

It is helpful to define financial priorities before making decisions from these calculations. This data are just tools that help you make decisions towards your goals

  • Do you have cash on hand for an emergency expense, and how much cash is reasonable for you?
  • How much risk are you taking with this position, considering your entire financial picture?

Holding the mortgage is a riskier position. Worst-case you can lose your home equity if the house is repossessed.

  • To what extent can you absorb the negative cash flow to access the increased return?
  • Is this position viable for you both now and in the future - even a future where your financial position is under stress from an unexpected event?

If I had your option as you presented it here, I would pay as much towards the mortgage as possible, minus cash for up to 6 months household expenses. I don't prefer to invest with borrowed money.

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All other things being equal and assuming there are no charges to make the complete payment towards the mortgage;

  1. If you loan is at 2.84% and your investments are yielding 7%; it
    makes sense to continue the loan. You would get better overall
    results monetary wise.
  2. Further the investment into CD's are risk free. So it does make sense to park it. The risk would have been different if you were investing in other products. So comparing CD's interest with Loan is right comparison and it looks better to continue the loan.
  3. Emergency Fund. Having cash in CD is always helpful incase of emergencies; paying off the mortgage would make it difficult to borrow [you can get HELOC kind of loans]; it would take time. So CD would win; and it makes sense to continue you mortgage
  4. Cash Flow. Paying off the mortgage would make it easy from cash flow point of view. More so you have a pressing need and want to improve the situation. Although one can achieve similar results using a CD ladder or flexible deposits; it becomes cumbersome to manage. So if you are not up to it; makes sense to pay off the mortgage
  5. Peace of Mind. If you feel the mortgage is a burden [it shouldn't be as you have cash equivalent]; then it would make sense to pay it of
  6. Plans to Sell off current home. It makes sense to close the mortgage, one can do it as part of sale; however the paperwork becomes more easier if you close the mortgage before the sale
  7. Untimely Death. This can be tricky; if you mortgage has waiver; i.e. the outstanding is written off [via some kind of insurance] then it is advantageous not be close it. If not your heirs will have to deal with paperwork to draw the funds from your savings and make the payment etc ... these things take time; the loan can meanwhile turn delinquent etc
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There are other ways of looking at the situation, I think, such as what would happen if you were hit with some unexpected emergency expense while your money was tied up in an investment and you no longer had the free cash flow to pay your mortgage, or whether your investment vehicle's return is guaranteed, or if there are penalties for early withdrawal, etc.

You're also not taking into account the effects of inflation. Today, your 82K is worth 82K in purchasing power, but next year, assuming inflation stays the same, that 82K will buy approximately 3% less than it does today. A year later, another 3%. After 3 or 4 years, your raw purchasing power is actually decreasing relative to 2018 dollars.

If I were in your shoes, I'd pay off the mortgage. Your cash will never be worth more than it is today, and you have the security of knowing that your housing payment is now a solved problem.

  • 1
    Total non-sequitur in that last paragraph. "Your cash will never be worth more than it is today" - So spend it. Interestingly enough inflation helps you a lot with your mortgage principal. The same 82k that would pay off your mortgage now would pay off your mortgage in 5 or 10 or even 30 years. Both decrease in value. Inflation can not be cited as a reason to pay off a mortgage early. (not that I necessarily disagree with you that it should be) – xyious Jun 26 '18 at 16:16
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As @jkuz says, the principal portion of your mortgage payment doesn't really belong in the "expense" category. After all, when you consider paying off the mortgage, you didn't include the $82k payment to your bank to be an "expense", did you? You're just moving money from the "bank account" category to the "home equity" category. Similarly, if you keep the mortgage, you'll have 710/month going towards your equity, and 195/month going towards carrying the loan (this mix will probably shift more towards the equity side as the year goes on, but we can ignore that). So the cost of the mortgage is the 195/month, or $2340/year. If you make $5740/year from your investments, then that's a net of $3400/year.

Result one year from now of paying off mortgage:
Cash: 0
Mortgage: 0
Equity: current equity + 82k
Total net worth: current equity + 82k

Result one year from now of keeping mortgage:
Interest payments: 2340
Principal payments: 8520
Investment income: 5740
Net cash flow: -5120
Starting cash: 82000
Final cash: 76880
Mortgage: 73480
Equity: current equity + 8520
Total net worth: current equity + 85400

  • It's important to note that there's some risk involved. The investments could lose value in the "keep the mortgage" scenario, leading to a total net worth of current equity - 10k (numbers vary). Clearly, paying off the mortgage now would be the better move in that scenario. OTOH, the investments could double over the course of the next year -- in that case, you'd kick yourself for paying off the mortgage instead of buying stocks/index funds. – Brian Jul 9 '18 at 22:44
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I consider the principal part of the payment in Scenario A as a sunk cost. If the payment is not a hinderance, it always makes sense to invest at 7% instead of paying off 2.84% in my eyes. Inflation is always a concern, but at 7% you're well out earning that increase.

I would think age would play a role in this decision as well. If you're in your twenties, you can afford to pay the mortgage off and then start funneling those mortgage payments into investment vehicles. If you're in your forties, it would make sense to invest the $82K because compound interest on that amount of money is going to increase much faster than starting from zero.

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