My finance professor repeatedly made the point that when evaluating an investment option, you must compare it to “something of similar risk.” He mentioned this in almost every class. 

Basic return formula: profit / investment. Two rules: Invest in positive NPV projects; Invest in projects offering return in excess of opportunity cost of capital. 

Example: Invest $1000 now, receive certain $1300 after 1 year
Assume investors can obtain 15% safe return
Decision: invest because 30% project return exceeds 15% opportunity cost; invest because present value of $1300 next year exceeds $1000 now. 
Present value = 1300/1.15 = 1130
Net present value = 1130-1000=+130

Perpetuity = constant payment forever; payment/rate
Example: you want to endow a chair at your old university. The aim is to provide $100k a year forever. The interest rate is 10%. 
Present value = $100,000 / .10 = $1,000,000. Therefore, a donation of $1MM provides $100K/year forever. 

Probably the most interesting and helpful thing to learn was how to use a financial calculator to figure out future and present values. I use a TI BA II Plus. Here’s an example: Say you’re planning to buy a new appliance in one year that you estimate will cost $3000, you’d want to know how much you need to set aside today to have $3K in one year. The interest rate is 8%. On my financial calculator, I enter the following sequence: 3000 FV > 8 I/Y > 1 N > 0 PMT > CPT PV. This results in the present value of $2777.78. The number is negative on the calculator because that’s the amount you have to invest today. 

Another calculator example, this one to figure out a monthly payment. You want to buy a new car for $35,000. The interest rate is 4% per year (which would be .33% per month). You plan to pay the car off in 5 years (60 months). What is your monthly payment? On calculator: 35000 PV > .33 I/Y > 60 N > CPT PMT. Payment is $689.82 per month. 

A house example. If you are buying a house for $103,000 on a 30 year note at 5% interest: 103000 PV > 5 I/Y > 30 N > CPT PMT. Gives a payment of $500 month towards the principle.