calculating number of periods

Example 1. Calculating Number of Periods – One of your customers is delinquent on his accounts payable balance. You’ve mutually agreed to a repayment schedule 0f $600 per month. You will charge 0.9 percent per month interest on the overdue balance. If the current balance is $18,400. How long will it take for the account to be paid off?

Using rule 72:

72/0,9 = 80 months

80 month = 3 years 8 months

Using Present Value Annuity (PV A):

PV A = c  x (1- 1/(1+r)^t)/r

$ 18,400 = $600 x (1 – 1 / (1+0.009)^t / 0.009

Solve the problem:

1/(1+0.009)^t = 1 – (($18,400)(0.009) / ($600))

1.009^t = 1/ (0.724)

t = ln 1.381 / ln 1.009

t = 36.05 months

t = 3 years 5 months

"at little india" 3 hours waiting for a bus 

Example 2. Waiting for godot. You’ve been saving up to buy the Godot Company. The total costs will be $10 million. You currently have about $2,3 million. If you can earn 5 percent on your money, how long will you have to wait? At 16 percent, how long must you wait?

At 5 percent, you’ll have to wait a long time. From the basic present value equation:

$2,3 million = $10 million / 1.05^t

1.05^t= 4,35

t = 30 years

reference:

Source: Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition.