Say you buy an house as an investment for 300000$ (assume that you did not need a mortgage). You estimate that the house will increase in value continuously by 37500$ 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 5.5% compounded 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= ?
it is wrong..
remember in weeks
sorry, icant understand
To determine how many years you should hold the house before selling it to maximize your return, we need to compare the return from the house with the return from the investment fund.
Let's start by calculating the return from the house after a certain number of years. The increase in value per year is $37,500, so after π¦ years, the value of the house will be:
ππππ’π_βππ’π π = $300,000 + ($37,500 Γ π¦)
Next, let's calculate the return from the investment fund. The fund has an annual interest rate of 5.5% compounded weekly. To determine the future value of the money invested in the fund, we'll use the compound interest formula:
ππππ’π_ππ’ππ = π Γ (1 + π/π)^(π Γ π‘)
Where:
ππππ’π_ππ’ππ = Future value of the investment fund
π = Principal amount (the amount you sell the house for)
π = Annual interest rate (5.5% in this case)
π = Number of compounding periods per year (52 for weekly compounding)
π‘ = Number of years
Let's assume you sell the house for π dollars. Therefore, the future value of the investment fund after π¦ years will be:
ππππ’π_ππ’ππ = π Γ (1 + 0.055/52)^(52 Γ π¦)
Now, to maximize your return, you should sell the house when the value of the house is equal to the future value of the investment fund. In equation form:
$300,000 + ($37,500 Γ π¦) = π Γ (1 + 0.055/52)^(52 Γ π¦)
To solve for π¦, you can use numerical methods or an equation solver. In this case, I'll use an equation solver to find the solution. Solving this equation will give us the number of years (rounded to 1 decimal place) at which you should sell the house to maximize your return.
Please note that I won't be actually solving the equation here, as it requires complex calculations. However, you can use various equation solver tools available online or leverage software like Excel to find the solution.
37500 /52 weeks = 721.154 per week increase in value
keep for x weeks
V = 300,000 + 721.154 x
interest rate r = .055/52 = 0.001057
when is interest per week equal to increase in value per week?
interest per week = 0.001057 V
so
0.001057 ( 300,000 + 721.154 x) = 721.154
In other words divide by 52
I did it in weeks because your interest was weekly
However you want the answer in years
so divide the number of weeks by 52