Engineering Economic Analysis

76 INTERESTAND EQUIVALENCE

Thus,

F =500(F j P,6%, 3)=500(1.191) =$595.50

Before leaving this problem, let's draw another-diagramof it, this time from the bank's point of

VIew.

Receipts(+)

P= 500

t

0-1-2-3

n=3 1

i==0.06 F=?

Disbursements (,--)

This indicates the bank receives $500 now and must make a disbursement ofF at the end of

3 years. The computation, from the bank's point of view, is II

F=500(F j P,6%,3) =500(1.191) =$595.50

This is exactly the Sameas what was computed from the depositor's viewpoint, since this is just

the other side of the same transaction. The bank's future disbursement equals the depositor's

future receipt.

If we takeF=P(l +i)nand solve forP,then

1

P=F =F(1 +i)-n

(1 +i)n

This is thesingle payment present worth formula.The equation

P=F(1 +i)-n (3-5)

in our notation becomes

P=F(PjF,i,n) (3-6)

If you wish to have $800 iri a savings account at the end of 4 years, and 5% interest was paid

annually, how much should you put into the savings account now?

, C~LUTION

F =$800 i- 0.05 n= 4 P=unJpIown

P =F(1+i)~n= 800(1 + 0.05)-4 = 800(0.8227) - $658.16

Thus to have $800 in the savings account at the end of 4 years, we must deposit $658.16 now.

II'

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