Calculating Future and Present value into mortgage comparisons
Keep in mind the number of months or years before you break even. You pay money to lower the interest rate, and lower the monthly cost. But it takes a number of months, using your numbers $7,000 to save $160 a month will take ~43 months. That is before figuring in the future or present value. If you sell or refinance the mortgage, the initial points to lower the rate is gone. You mentioned 15-20 years in your comment on mhoran_psprep's response. This is the most important factor to consider in the points vs. rate question. With a horizon that long it sounds like the points are probably a better option for you. There is a neat comparison tool at The Mortgage Professor's website that may help you build your spreadsheet or simply check the numbers you are getting. "Using the fact that you'd save $160/mo by spending $7000, I'd look at it this way -  If I were to lend you the $7000 at 12%/yr, $160 would pay it off in 58 months. At 18%/yr, 72 months or just 6 years. You can run spreadsheets to get breakeven scenarios, and mhoran is on track with his answer, but breakeven is just one point to consider. Beyond that date, it's free money.  My approach is to look at it with a question - ""How much interest could I afford to pay to make that monthly savings worthwhile?"""
"derivatives!  learn about how they are priced, traded, and used within a portfolio for hedging and speculating.  there are calculators for ""net present value calculations,"" and you are never going to walk into an interview and say, ""Hey! I can look at a formula and price something.""" Cap rate includes any interest on the mortgage and not the repayments of the mortgage. Cap rate represents the net income which is the gross rent minus all costs, including the interest on the loan. Mortgage repayments form part of your cash flow calculations not your return calculations. ROI is a calculation which works out your net income over the initial investment you made, which is you downpayment plus costs and not the value of the property. The short answer is you'd be much better off paying up front in this case.  The present value of $2,500 plus 12 $500 monthly payments is $8,128 at a 12% discount rate, which is much higher then the $6,000 you could pay now. The long answer is how you get that present value.  How can I use time value of money to find the present value of money if I choose to go with option A? First of all, I'd question your discount rate.  A 12% discount rate means that you can safely reinvest the money that you're not spending today at a 12% annual (1% monthly) rate, which seems very high.  Normally for short-term spending decisions you'd use a risk-free rate, which would be closer to 1%-2%. However, to discount at 1% monthly you'd just divide each monthly payment by 1 plus the discount rate raised to the power of the number of periods until each payment. So the total is which is $8,127.54 You could also use the NPV function in Excel. It seems like to get an accurate answer the calculation of the interest rate should take into account compounding period as well? Correct, and in the example above the compounding is assumed to be monthly since that's the periodicity of the cash flows. You could calculate it with a different compounding period but it gets much more complicated and probably wouldn't make a significant difference. The discount rate does take compounding into effect, meaning if you saved the $5,628 (the PV of $8,128 minus the $2,500 initial payment), you'd earn 1% interest on $5,628 the first month, $5,128 plus that interest the second month, etc. "Currently, when ""implied volatility"" is spoken, the Black-Scholes-Merton model is implied.  This model has been shown to be deficient, thus the Variance Gamma Model should be used. However, as nearly no one uses VG, it can be assumed that BS is still being implied. The BS formula has multiple variables.  Some are external to the underlying in question.  The rest are internal. When all but one variable is known or assumed, the last variable can be calculated, so if one has the price of the underlying and all else except the volatility, the volatility can be calculated thus implied. If one selects an implied volatility, and all variables except the underlying price is known, the underlying price can be calculated. For the present, one uses the current price of the underlying to calculate the implied volatility.  For future option prices, one assumes an implied volatility at a later date to calculate a possible price. For prices not at the money, the BS model is extremely imprecise.  The VG model can better determine a potential future price." I use a spreadsheet for that.   I provide house value, land value, closing/fix-up costs, mortgage rate and years, tax bracket, city tax rate, insurance cost, and rental income.  Sections of the spreadsheet compute (in obvious ways) the values used for the following tables:  First I look at monthly cash flow (earnings/costs) and here are the columns:   Next section looks at changes in taxable reported income caused by the house,  And this too is monthly, even though it'll be x12 when you write your 1040.   The third table is shows the monthly cash flow, forgetting about maintenance and assuming you adjust your quarterlies or paycheck exemptions to come out even: Maintenance is so much of a wildcard that I don't attempt to include it.  My last table looks at paper (non-cash) equity gains:  I was asked how I compute some of those intermediate values.  My user inputs (adjusted for each property) are:  My intermediate values are: I am currently trying out some variations (moving terms around ...) of the formula for the present value of money The relationship between yield and price is much simpler than that. If you pay £1015 for a bond and its current yield is 4.69%, that means you will receive in income each year: 4.69% * £1015 = £47.60 The income from the bond is defined by its coupon rate and its face value, not the market value. So that bond will continue to pay £47.60 each year, regardless of the market price. The market price will go up or down according to the market as a whole, and the credit rating of the issuer.  If the issuer is likely to default, the market price goes down and the yield goes up. If similar companies start offering bonds with higher yields, the market price goes down to make the bond competitive in the market, again raising yield. So if the yield goes up to 4.87%, what is the price such that 4.87% of that price is £47.60? £47.60 / 4.87% = £977.48 Another way to think of it: if the yield goes up from 4.69% to 4.87%, then yield has increased by a factor of: 4.87% / 4.69% = 1.0384 Consequently, market price must decrease by the same factor: £1015 / 1.0384 = £977.48 If you are using an Excel, the Function PV should be able to easily calculate this. Excel Formulae PV = (Rate,Nper,Pmt,Fv,Type)   Where Rate: Rate of return. In this case you can use Inflation or assumed rate that would cost you. Say 3-5%. Note the Rate has to be for Nper. i.e. in Nper if you are counting yearly payments, then rate is yearly, if you are counting as monthly, then the rate should be monthly.   NPer: Number of periods. If yearly in your case it would be 20. If Monthly 20*12, if Quarterly 20*4 etc.   Pmt: Expected Payments for Nper. If you are saying 20 million over 20 years, it would be 1 million per year. Fv and Type can be blank So assuming a rate of 3%, and yearly payments of 1 million over 20 years. PV = $14,877,474.86 [It would show negative, just ignore the sign] "As Michael McGowan says, just because gold has gone up lots recently does not mean it will continue to go up by the same amount. This plot:  shows that if your father had bought $20,000 in gold 30 years ago, then 10 years ago he would have slightly less than $20,000 to show for it. Compare that with the bubble in real estate in the US:  Update: I was curious about JoeTaxpayer's question: how do US house prices track against US taxpayer's ability to borrow?  To try to answer this, I used the house price data from here, the 30 year fixed mortgages here and the US salary information from here. To calculate the ""ability to borrow"" I took the US hourly salary information, multiplied by 2000/12 to get a monthly salary. I (completely arbitrarily) assumed that 25 per cent of the monthly salary would be used on mortgage payments.  I then used Excel's ""PV"" (Present Value) function to calculate the present value of the thirty year fixed rate mortgage. The resulting graph is below.  The correlation coefficient between the two plots is 0.93.  There are so many caveats on what I've done in ~15 minutes, I don't want to list them... but it certainly ""gives one furiously to think"" !! Update 2:  OK, so even just salary information correlates very well with the house price increases.  And looking at the differences, we can see that perhaps there was a spike or bubble in house prices over and above what might be expected from salary-only or ability-to-borrow."