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?

Guest Feb 6, 2020

#1**+2 **

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.

ElectricPavlov Feb 6, 2020