Question

You are trying to decide a present worth of a contract. You will receive $10,000 when the contract is signed, a $20,000 payment at the end of Year 1, and $30,000 at the end of Year

2, and $40,000 at the end of Year 3, and $50,000 at the end of Year 4 when the project is completed. Your annual costs for this project are $10,000 per year. What is the present

worth of the contract at 5%? Must use gradient method.

A building is priced at $105,000. If a down payment of $15,000 is made and payments of $3,005 every 3 months thereafter are required, how many years will be necessary to pay

for the building? Interest is charged at 4% compounded quarterly.

Answer 1

1.

NPW of project = 10000 + 20000 *(P/A,5%,4) + 10000 *(P/G,5%,4) - 10000 * (P/A,5%,4)

= 10000 + 10000 *(P/A,5%,4) + 10000 *(P/G,5%,4)

= 10000 + 10000 *3.545951 + 10000 *5.102812

= 96487.62

2.

i = 4% / 4 = 1% per quarter

let n quarters will be required for payoff

105000 = 15000 + 3005 *(P/A,1%,n)

3005 *(P/A,1%,n) = 105000 - 15000 = 90000

(P/A,1%,n) = 90000 / 3005 = 29.950083

((1 + 0.01)^n-1)/(0.01 * (1 + 0.01)^n) = 29.950083

(1.01)^n - 1 = 29.950083 * 0.01 * (1.01)^n

1.01^n = 1 / (1 - 0.29950083) = 1.42755344

taking log both sides

n = log 1.42755344 / log 1.01 = 35.77 quarters

No. of yrs = 35.77 / 4 = 8.94 yrs ~ 9 yrs