Question

at the end of 5 years? What if the appreciation rate is 0%? (2) You purchase an apartment building with 20 rentable units. You know that you will have to replace the air conditioners in each unit 10 years from now at a cost of $1,500/unit. How much money should you put away at the end of every year, in a bank account earning 6%, to have enough money to replace the air conditioners in 10 years

Answer 1

Let the amount deposited each year be P

Number of years = n = 10

Total Amount required after 10 years = FV = number of units * cost per unit = 20*1500 = $30000

Interest rate = r = 6%

Hence, FV = P(1+r)^n-1 +....+ P(1+r)² + P(1+r) + P = P[(1+r)ⁿ -1]/r

=> 30000 = P[(1+0.06)¹⁰ -1]/0.06

=> P = 30000*0.06/[(1+0.06)¹⁰ -1] = 2276.04

Hence, he should keep away $2,276.04 each year to save for replacement of 20 air conditioners after 10 years