Answer:
3.3 years
Step-by-step explanation:
Let the price of the house when it is being sold be = x
The Annual return received from the fund after a year that house is being sold is : A - P
where ;
P = current market price
A = price after one year
A is given by the formula:
[tex]A = P (1+ \frac{r}{n} )^{{n}{t} }[/tex]
where ; P = x
r = 8.5% = 0.085
n = 12
t = 1
[tex]A= x(1+\frac{0.085}{2})^{12*1}[/tex]
[tex]A= x(1.00708333)^{12}[/tex]
A = 1.08839 x
The annual return is A - P = 1.08839 x - x
= 0.08839x
However, the house should be sold when this return is equivalent to the annual increase in value of the house
∴ 0.08839x = 31250
[tex]x = \frac{31250}{0.08839} \\ \\ x = 353546.78[/tex]
Thus , the current price (x) = $353546.78
Profit till that time = Current price - Initial Price
= (353546.78- 250000)$
= $103546.78
The time taken for this much profit to accumulate = [tex]\frac{Total \ profit}{Annual \ profit}[/tex]
= [tex]\frac{103546.78}{31250}[/tex]
= 3.3135
≅ 3.3 years ( to one decimal place)
