Problem $6$

A couple in Regina, Saskatchewan, must decide whether it is more economical to buy a home or to

continue to rent.

The couple rents a one$-$bedroom duplex for $$460$ a month plus $$100$ per month for basic utilities.

Rent is expected to rise $2\mathrm{.}5\%$ each year, and utilities are expected to rise $5\%$ each year. Rent and

utilities costs only rise at the end of each year. So in year $1,$ for example, the rent will be $$460$ each

and every month. But the rent will be higher in year $2,$ and so on$.$

The couple is considering buying a home that costs $$94,000.$ A local mortgage company will provide

a loan that requires a down payment of $5\%.$ If they buy the house, the realtor will also charge a sales

commission of $5\%$ of the value of the purchase, payable immediately. The couple would select a $25-$

year fixed$-$rate mortgage with an $7\%$ interest rate. It is estimated that the basic utilities, home insurance,

and maintenance costs will be $$300$ each month, and will rise $4\%$ every year $($but will only rise once

per year, at the end of the year$).$ The home is expected to appreciate in value $3\mathrm{.}5\%$ a year. If they buy

a home, assume they will sell it in $15$ years.

$($a$)$ Choose a discount rate to apply for net present worth analysis. Justify your decision to choose

this discount rate.

$($b$)$ Analyze both options using net present worth analysis, using an annual time step $($rounded to

the nearest dollar$).$ Which alternative should the couple select?

$($c$)$ The problem is missing a piece of information that you would need to properly assess the

options. What is it$,$ and why is it necessary?