Engineering Economic Analysis

118 MORE INTERESTFORMULAS

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How long will it take for money to double at 10% nominal interest, compounded continuously?

F=Pern

2 = 1 eO.IOn

eO.IOn = 2

or

O.lOn= 102 = 0.693

n= 6.93 years

It will take 6.93 years for money to double at 10% noniinal interest, compounded continuously.

If the savings bank in Example 4-14 changed its interest policy to 6% interest, compounded

continuously, what are the nominal and the effectiveinterest rates?

• SOLUTION

The nominal interest rate remains at 6% per year.

Effective interest rate=er- 1

=eO.06- 1 =0.0618

=6.18%

..:.

Uniform Payment Series: Continuous Compounding

at Nominal Raterper Period

Let us now substitute the equation i=er- 1 into the equations for end-of-period

compounding.

Continuous Compounding Sinking Fund

er-1

[AI F, r, n]=ern _ 1 (4-41)

Continuous Compounding Capital Recovery

ern(er- 1)

[AlP, r,n]= ern- 1 (4-42)

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