Say you buy an house as an investment for 400000$ (assume that you did not need a mortgage). You estimate that the house will increase in value continuously by 50000$ per year. At any time in the future you can sell the house and invest the money in a fund with a yearly interest rate of 8.5% compounded semiannually. If you want to maximize your return, after how many years should you sell the house?
Simple interest will result in the following amount after 'x' years
400 000 + 50 000 x
If you invest in the fund you will have
400 000 (1 + .0425)^2x interest is .0425 for each 1/2 year ( 1/2 of .085 )and there are 2 periods for each x years)
When does your accumulated total earn more money compounded than 50 000 year?
50 000 < (400 000 + 50 000 x) (1.045)2 - (400 000 + 50 000x)
436 810 + 54601.25x - 400 000 - 50 000 x
36810 + 4601.25x
13190 < 4601.25x
2.8667 < x ~~ at 3 years the fund account would make more money that 50 000 a year
at end of 3 years you would have 550 000
at end of 4 years 600 000 if you put that money into the fund, at the end of 4 years you would have
550 000 (1.045)^2 = 600 613.75
All of this says At the end of 3 years , put your money in the fund.