Engineering Economic Analysis

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112 MORE INTERESTFORMULAS

annually, the nominal interest rate equals the effective interest rate. Also, it will be noted

thatincreasingthe frequencyof compounding (for example,from monthly to continuously)

hasonly a small impact on the effective interest rate. But if the amount of money is large,

evensmall differencesin the effective interest rate can be significant.

Aloan shark lends money on the following terms: "If I give you $50 on Monday, you owe me

$60 on the following Monday."

(a) What nominal interest rate per year(r) is the loan shark charging?

(b) What effectiveinterestrateper year(ia)is he charging?

(c) If the loan shark started with $50 and was able to keep it, as well as all the money he

received, out in loans at all times, how much money would he have at the end of one

year?

F= P(FjP, i, n)

60 = 50(F j P, i, 1)

(FjP, i,1)=1.2

Therefore, i=20% per week.

Nominal interest rate per year=52 weeks x 0.20=10.40=1040%

Effectiveinterest rate per year ia= (1 + ~) m- 1

(

10.40

)

52

= 1 + 52 - 1= 13,105- 1

= 13,104- 1,310,400%

Or

Effective interest rate per year ia=(1 +i)m~ 1

I

• (1 + 0.20)52- 1= 13,104


• 1,310,400%

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