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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?

 Feb 6, 2020
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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.

 Feb 6, 2020

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