I always tell people that back-of-envolop calculation is as good as any other complex ones for decision making. When we calculate NPV, we can simply use above 7-10 rule. The reason for 7-10 rule is that
(1+7%)10 ~= 2
In another word, if the interest rate is 7%, over 10 years, you will double your money.
So, when you try to figure out how to double your money, use
Interest Rate x Number of Years = 70
So,
for 7% interest rate, 70/7=10 year will double your money
for 5% interest rate, 70/5=14 year will double your money
for 10% interest rate, 70/10=7 year will double your money
BTW, to be more exact, it 72, not 70, since
(1+7%)(72/7) = 2.005548
but 70 is much easier to use.
Go back to our Lottery example, if you win $1M lottery and choose to take one lump sum payment, you will get ~ $500K USD (for simplicity, let's ignore tax here.). You then invest those money in ETF (say QQQQ) that have average return of 7% per year.
In 10 years, you will have $500K x 2 = $1M
In 20 years, you will have $500K x 2 x 2 = $2M
In 30 years (roughly 26 years), you will have $500K x 2 x 2 x 2 = $4M
Power to the time (Time = money).
Remember, if you choose annual payment, you will get $1M over 26 years in California. Of course, you should also invest those annual payment in ETF as well. That will be homework for you to figure out what you would get by the end of 30 years.
You can do the same to estimate how much interest you are paying for your mortgage. Say, you borrow $500K at a rate of 5% for 30 year fixed rate mortgage,
based on 7-10 rule, 70 / 5 = 14
so, in 14 years, bank double the money; in 28 years (roughly equal to 30 years), bank get 4x of the original $500K (called principle). It basically says that your mortgage is roughtly worth $2M at the end of 30 years.
Of course, since you pay interest to bank over time, not in a lump sum at 30 years down the road, you do not pay $1.5M interest to the bank (bank will tell you that you roughtly pay 1/3 of that, or $500K interest during the life of the loan.). But the total value of interest you paid to the bank is $1.5M at 30 years down the road.
Now we had fun with NPV. Let's look at the problem from another angle, which is Internal Rate of Return (IRR).
