Question

You would like to buy a new computer. You see in a magazine advertisement that you can get a new 2.4 GHz Athlon computer system for $1,600. Alternatively, the ad says you can lease the computer for $56 a month. The lease would last 36 months, after which you would have the option to buy the computer for 10% of the original purchase price. Assuming you will purchase the computer at lease end, what annual rate of interest are you paying under the lease arrangement? (Hint: Think of yourself as issuing a bond to buy the computer.)

PLEASE SHOW ALL WORK AND FORMULAS FOR EACH PART

Answer 1

Cost of Computer = 1600 = current value

Lease rate = 56 per month

Lease Term = 36 months

Future Value = 10% of original price = 160

If we are opting for lease arrangement, then we can consider it at issuing a bond with :

Current Price(p) = 1600

Future price(f) = 160

Coupon payment (c)= 56

Time(n) = 36 month

monthly Interest rate(r) =????

p = c / (1+r)^1 + c / (1+r)^2 + c / (1+r)^3 +............................ + (c+f) / (1+r)^36

1600 = 56 / (1+r)^1 + 56 / (1+r)^2+ ..................................+ (56+160) / (1+r)^36

By hit and trial :

r = 1.649

Annual r = 1.649 * 12 = 19.8%

We can find r in financial calculator as well as using rate() function in excel.