Say you buy an house as an investment for 250000$ (assume that you did not need a mortgage). You estimate that the house will increase in value continuously by 31250$ 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 bi-monthly.

If you want to maximize your return, after how many years should you sell the house? Report your answer to 1 decimal place.

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:

where ; P = x

r = 8.5% = 0.085

n = 12

t = 1

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

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 =

=

= 3.3135

≅ 3.3 years                 ( to one decimal place)

circumference divided by 3.141592654 then timesthe radius twice

step-by-step explanation:

circumference divided by 3.141592654 then timesthe radius twice

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form