“Being able to calculate” is fine (though I’d like a more clear test that doesn’t require the user to generate random numbers), but “being able to explain” is not nearly crisp enough. It’s almost as bad as using “being able to explain why politics is the mind-killer” as part of a test for rationality. Could you rethink that part?
You should be able to figure out how much money you will pay in compound interest on a loan, or how much you will earn on an interest bearing account, in a fixed amount of time.
You should be able to compare the monetary values of different financial decisions (e.g. borrowing money, paying off a loan, purchasing an investment) by comparing their present value.
Suppose you can have $100 today or $100 in a year. Since you could do things with the $100 in between, but you could also choose to hold onto it for a year if that turns out to be a better idea, you’re likely to prefer $100 today. But most people would take $1,000,000 in a year over $100 today, so the value of getting money a year earlier is finite.
If you are indifferent between $105 in a year and $100 today—i.e. if a 5% return on the money would exactly compensate for a year’s delay—then we say your annual “discount rate” is 5%, and the “present value” of $105 next year is $105 / (100%+5%) = $100. Finance generally assumes that discount rates are constant, and compound just like interest.
To give a simplified example of where this is useful, suppose you are deciding whether to buy a home for $100,000 (in cash) or rent a home for $10,000 per year, payable at the end of the year. Your discount rate is 5%. As simplifying assumptions, suppose no transaction costs, you know you will live there for exactly 10 years, and neither the home’s value nor the rent would change after that time period.
The present value of $-100,000 now is obviously $-100,000. But you could sell the house in 10 years for a present value of $100,000 / (1.05^10) = $61,391.33, so the net present value of buying is the revenue minus the cost, $61,391.33 - $100,000 = $-38,608.67
The present value of the rent over 10 years is the sum from i = 1 to 10 of $-10,000 / (1.05^i) = $-77,217.35. So in this example buying is much cheaper than renting.
In a real life buy-vs-rent calculation, you have to deal with complicating factors like the amortization of mortgages, but you can deal with most complications by calculating the present value of each component separately. That’s what I did in my own buy-vs-rent calculation.
Thanks! For what it’s worth, I was missing the part where everyone has a personal discount rate. If I’m allowed to assume that, then everything becomes obvious, of course.
If you don’t mind, I have edited the finance part to say “make a buy vs rent calculation, using prices appropriate for your area and your current standard of living”. That sounds more crisp to me than “be able to do something”.
“Being able to calculate” is fine (though I’d like a more clear test that doesn’t require the user to generate random numbers), but “being able to explain” is not nearly crisp enough. It’s almost as bad as using “being able to explain why politics is the mind-killer” as part of a test for rationality. Could you rethink that part?
OK, here’s my revised version for finance:
You should be able to figure out how much money you will pay in compound interest on a loan, or how much you will earn on an interest bearing account, in a fixed amount of time.
You should be able to compare the monetary values of different financial decisions (e.g. borrowing money, paying off a loan, purchasing an investment) by comparing their present value.
It must be telling of my financial ignorance that I don’t understand the second part :-( Could you give an example?
Suppose you can have $100 today or $100 in a year. Since you could do things with the $100 in between, but you could also choose to hold onto it for a year if that turns out to be a better idea, you’re likely to prefer $100 today. But most people would take $1,000,000 in a year over $100 today, so the value of getting money a year earlier is finite.
If you are indifferent between $105 in a year and $100 today—i.e. if a 5% return on the money would exactly compensate for a year’s delay—then we say your annual “discount rate” is 5%, and the “present value” of $105 next year is $105 / (100%+5%) = $100. Finance generally assumes that discount rates are constant, and compound just like interest.
To give a simplified example of where this is useful, suppose you are deciding whether to buy a home for $100,000 (in cash) or rent a home for $10,000 per year, payable at the end of the year. Your discount rate is 5%. As simplifying assumptions, suppose no transaction costs, you know you will live there for exactly 10 years, and neither the home’s value nor the rent would change after that time period.
The present value of $-100,000 now is obviously $-100,000. But you could sell the house in 10 years for a present value of $100,000 / (1.05^10) = $61,391.33, so the net present value of buying is the revenue minus the cost, $61,391.33 - $100,000 = $-38,608.67
The present value of the rent over 10 years is the sum from i = 1 to 10 of $-10,000 / (1.05^i) = $-77,217.35. So in this example buying is much cheaper than renting.
In a real life buy-vs-rent calculation, you have to deal with complicating factors like the amortization of mortgages, but you can deal with most complications by calculating the present value of each component separately. That’s what I did in my own buy-vs-rent calculation.
Thanks! For what it’s worth, I was missing the part where everyone has a personal discount rate. If I’m allowed to assume that, then everything becomes obvious, of course.
If you don’t mind, I have edited the finance part to say “make a buy vs rent calculation, using prices appropriate for your area and your current standard of living”. That sounds more crisp to me than “be able to do something”.
Thanks, that probably made it much clearer.