Question

Mike is considering renting a new apartment for a total of 4 years. Rent will be paid monthly starting at $2,460 with the first payment in one months' time. The rental contract states that the rent will increase each month at the inflation rate of 2% p.a. compounded annually. If the appropriate discount rate is 6.25% p.a. compounded annually, what is the total cost to Mike of this rental agreement in current terms?

Answer 1

first we have to calculate monthly rate for annual compounding

let x = monthly rate

Effective annual rate = (1+x)^n - 1

x = monthly rate

inflation:

(1+x)^12 - 1 = 2%

x = (1+2%)^(1/12) - 1

x = 0.1652%

Discount rate:

(1+x)^12 - 1 = 6.25%

x = (1+6.25%) ^(1/12) - 1

x = 0.5065%

Present value of growing annuity = [P/(r - g)]*[1 - [(1+g)/(1+r)]^n]

P = monthly rent

r = monthly discount rate

g = monthly inflation rate

n = number of periods = 4*12 = 48

Present value = [2460*/(0.5065% - 0.1652%)]*[1 - [(1+0.1652%)/(1+0.5065%)]^48]

= $108,579