Question

Suppose you have cash on hand in the amount of d dollars and wish to buy a house. Assume that you want to have a down payment of 10% of the house price, and transactions costs are 8% of the house price. Also, suppose a payment of R dollars per month pays off a mortgage loan of 217.39R dollars in 25 years.

(a) Express the house price you can afford as a function of the cash on hand d.

(b) Express the monthly mortgage payment required as a function of the cash on hand d.

(c) Express the cash on hand required as a function of the monthly mort- gage payment you can afford.

Answer 1

Suppose you have cash on hand = d dollars

This cash on hand is equal to down payment of 10% of the house price

That means

Down payment of 10% of the house price = d

House price = d/10% = 10 d

Transactions costs are 8% of the house price = 8% * 10 d = 0.8 d

Therefore mortgage loan = House price + Transactions costs – down payment

= 10 d + 0.8 d – d = 9.8 d

But we know that mortgage loan = 217.39R

Where R is the monthly mortgage payment

Therefore,

9.8 d = 217.39R

Or R = 9.8 d / 217.39 = 0.045d

Or d = 217.39R/9.8 = 22.18R

Now we can easily answer following questions

(a) Express the house price you can afford as a function of the cash on hand d.

House price = d/10% = 10d

(b) Express the monthly mortgage payment required as a function of the cash on hand d.

R = 9.8 d / 217.39 = 0.045d

Where R is the monthly mortgage payment

(c) Express the cash on hand required as a function of the monthly mortgage payment you can afford.

d = 217.39R/9.8 = 22.18R

Where d is the cash on hand and R is the monthly mortgage payment