A company is looking at three different machines as shown to buy. If the interes

Question

A company is looking at three different machines as shown to buy. If the interest is 8%, which machine should be selected if the present worth analysis is used? A customer in need of money machine comes to Payday Loan company to borrow $1,000. This company will charge the customer $120 interest if the total amount of $1,120 is paid no more than 1 week after the loan is made. Determine: (1) nominal annual interest rate and (2) the effective annual interest rate that the customer will pay on this loan?

Explanation / Answer

1

Since, the duration of machine life is unequal, we calculate the Equivalent Annualized Present Worth [EAPW].

EAPW = P.W. of Machine / PVIFA(8%,n)

E.A.P.W. Machine 1 = [40,000 + 9,000*PVIFA(8%,2)]/PVIFA(8%,2)
= [40,000 + 9,000*1.7833]/1.7833
= $31,430.33

E.A.P.W. Machine 2 = [80,000 + 6,000*PVIFA(8%,4)]/PVIFA(8%,4)
= [80,000 + 6,000*3.3121]/3.3121
= $30,153.86

E.A.P.W. Machine 3 = [130,000 + 4,000*PVIFA(8%,8)]/PVIFA(8%,8)
= [130,000 + 4,000*5.7466]/5.7466
= $26,622.07

THUS, WE SELECT MACHINE 3 AS IT HAS THE LOWEST EAPW

2

Effective Weekly Interest Rate = 120/1000 = 12%
Nominal Annual Interest Rate = Effective Weekly Interest Rate*52
= 12%*52 = 624%

Effective Annual Interest Rate = (1+ Effective Weekly Interest Rate)52 - 1
= (1 + 12%)52

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