Time Value of Money: The Buy Versus Rent Decision

1. Without considering other fees, the total mortgage loan, after down payment, is 80% of $600,000.

First convert the interest rate to compounding monthly,

(1+0.04/2)2 = (1+APR/12)12

=> APR = 0.03967

=> interest rate per monthly compounding period = 0.03967/12 = 0.0033058

Next, 600,000 x 0.8 = C x (PVA) , where C = monthly mortgage payment

= C x [ 1 – (1/1+0.0033058)^(25x12)] / 0.0033058

=> Monthly mortgage payment, C = $2,524.7

2. Note the original funds for investing are:

(i) down payment 0.2 x $600,000 (ii) 1.5% local deed-transfer tax (iii) 1.5% provincial deed-transfer tax

Opportunity cost = Monthly benefit from investing and earning monthly interest rate 0.0033058

= (600,000 x (0.2 + 0.015 + 0.015) + 2000) x 0.0033058

= $462.8

3.Monthly cost for rent = 3000

Monthly cost for purchasing = 2524.7 + +1055 + 300 + 600/12 + 462 = 4391.7

(Note: for purchasing costs also include monthly condo fee, property tax and monthly maintenance)

=> Additional payment required to buy over rent = 4391.7 – 3000 = $1391.7

4. Principal outstanding = 600,000 x 0.8 – 2524.7 PVANx12

= (600,000 x 0.8 – 2524.7 x [ 1 – (1/1+0.0033058)^[(N)x12]]) / 0.0033058) x (1+0.0033058)^(Nx12)

a. for N = 2

Principal outstanding = $456,713.2

b. for N = 5

Principal outstanding = $417,969.1

c. for N = 10

Principal outstanding = $342,232.4

5. a. The condo price remains unchanged ($600,000).

Net gain = 600,000 – 600,000x(1+0.0033058)^12

= - $24,239.3

Gross gain = 600,000 – 342,232.4 = 257,767.6

Net

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