Question

Say you buy a house as an investment for 500000$ (assume that you did not need a mortgage). You estimate that the house will increase in value continuously by 62500$ per year. At any time in the future you can sell the house and invest the money in a fund with a yearly interest of 6.5% compound weekly. If you want to maximize your return, after how many years should you sell the house? Report your answer to 1 decimal place. years=?

Answer 1

Let the price of the house, when it is sold be x.

Therefore, the annual return got through the fund one year after the house is sold is -

A - P

where P = x is the current price

And A is the price after 1 year given by

A = P(1+r/n)nt

P = x

r = 0.065

n = 52 (number of weeks in a year)

t = 1

Therefore,

A = x(1+0.001250)52

A = x*1.00125052

A = 1.067116x

Therefore, the annual return is A - P = 1.067116x- x = 0.067116x

The house should be sold when this return is equal to the annual increase in value of the house

Therefore

0.067116x = 62500

x = 62500/0.067116 = 931223.55

Therefore, profit till that time = Current price - Initial price = 931223.55- 500000= 431223.55

Time take for this much profit to accumulate = Total profit / Annual profit = 431223.55/ 62500= 6.899

Therefore, the house must be sold after 6.899 years.