HELP ANSWER PART F$$Problem $3$: Looking to Buy$$A former NYU Stern Professor $$John$($this one is a true story$)$ recently asked for advice on purchasing a property in Massachusetts. He was looking at a property similar to $80$ Captains Row, Bourne, MA $02532.$ Look up the $80$ Captains Row property on Zillow. $$a$)$ Notice that the $$zestimate$$ Zillow$$s best estimate of the house price $$ jumps in July $2018.$ Can you figure out why Zillow$$s formula to estimate prices would predict such a large increase? Do you think the variable that accounts for this increase should be in their formula to estimate the price?$$The jump in Zillow's "Zestimate" for a property like $80$ Captains Row, Bourne, MA $02532,$ in July $2018$ could be due to several factors:Whether the variable responsible for this increase should be included in Zillow's formula depends on the specific circumstances. If the jump in value was due to a temporary or unusual event, it may not be appropriate to include it as a permanent variable in the estimation formula. If the increase reflects a genuine change in the property's value that is likely to persist, then including it in the formula could lead to more accurate estimates.$$b$)$ Suppose that John put $20\%$ down and paid $$1\mathrm{.}3$m on the property. Using the estimate for $30$ FRM rates you gathered earlier $($in short question $2),$ estimate the monthly payment for a $30-$year fixed rate mortgage on this property.$$To estimate the monthly payment for a $30-$year fixed$-$rate mortgage $($FRM$)$ on a $$1\mathrm{.}3$ million property with a $20\%$ down payment, you can use the formula for calculating the monthly payment of a fixed$-$rate mortgage:$$MM $-$ is the monthly payment.PP $-$ is the principal amount $(80\%$ of $$1\mathrm{.}3$ million, which is $$1,040,000).$Rr $-$ is the monthly interest rate $($annual rate divided by $12$ months$).$Nn $-$ is the total number of payments $(30$ years $*12$ months per year $=360$ payments$).$Estimate for the $30-$year FRM rate you gathered earlier for Rr$.$ Let us assume an annual interest rate of r $=3\mathrm{.}5\%/12$M$=1,040,000(0\mathrm{.}002917(1+0\mathrm{.}002917)360/(1+0\mathrm{.}002917)3601)$M $$ $$4,661\mathrm{.}19$The estimated monthly payment for the $30-$year fixed$-$rate mortgage is approximately $$4,661\mathrm{.}19$c$)$ Suppose that John has the money to pay for the property in cash, or get a mortgage. Factoring in the interest deduction $($at a $37\%$ tax bracket$)$; how much will John have paid in total for the mortgage after $30$ years?$$Total Mortgage Payments $=$ Monthly Payment $*$ Total Number of Payments Total Mortgage Payments $=$ $$4,661\mathrm{.}19*360$ Total Mortgage Payments $$ $$1,679,928\mathrm{.}40$d$)$ If John could instead reinvest the cash somewhere else $$ what rate of return would John need on the alternate investment for it to make sense to get the mortgage instead of paying fully in cash?$$The mortgage cost is the total interest paid over $30$ years, which you calculated in part $($c$)$ as approximately $$1,679,928\mathrm{.}40.$ Let us assume John can invest the cash elsewhere and expects an annual return rate of R$\%.$Future Value $=$ Present Value $*(1+$ Rate of Return$)^$Number of YearsFutureValue$=1,679,928\mathrm{.}40(1+$R$100)30$Now$,$ compare this future value to the expected return on the investment. John would be better off getting the mortgage if the expected rate of return on the investment is higher than the future value of the mortgage cost.e$)$ Suppose the property has a $$14$k$/$year flood insurance requirement if the property has a mortgage. How does your answer to d change?$$If the property has a $$14,000$ per year flood insurance requirement due to having a mortgage, it would increase the total cost of owning the property with a mortgage. To incorporate this additional cost into the calculation from part $($d$),$ you would need to add the annual flood insurance cost to the mortgage cost for each year. Then, calculate the future value of this increased cost and compare it to the expected return on the investment.$$f$)$ Should John get the mortgage?