Engineering Economic Analysis

Continuous Cpmpounding 119

Continuous Compounding Series Compound Amount

ern- 1

[F/A,r,n] = er-l (4-43)

Continuous Compounding Series Present Worth

ern - 1

[P/A, r, n]= ern(er _1)

(4-44)

In Example 4-1, a II.1andeposited $500 per year into a credit union that paid 5% interest, com-

pounded annually. At the end of 5 years, he had $2763 in the credit union. How much would he

have if the institution paid 5% nominal interest, compounded continuously?

. ,.,SOLUTION. -. " '! ...~..'- '-",.-~;""~~

A=$500 r=0.05 n=5 years

(

ern _ 1

) (

eOo05(5)- 1

)

F=A[F/A,r,n]=A er- 1 =500 e (^005) 0 - 1
=$2769.84
He would have $2769.84.
In Example 4-2, Jim Hayes wished to save a uniform amount each month so he would have $1000
at the end of a year. .Based on 6% nominal interest, compounded monthly, he had to deposit
$81.10 per month. How much would he have to deposit if his credit union paid 6%.nominal
interest, compounded continuously?
'. .. ,.. .,.,....
SOLUTlO~;;
The deposits are made monthly; hence, there are 12 compounding subperiods in the one-year time
period. : =;;;; ~
.. .'. 0.06
r= nommal mterest rate/mterest penod=~ - 0.00^5
12
n =12 compounding subperiods iQ the one-year geri9PQfJhe PJohl~,n:1.
F=$1000
= ~ ::

• -_ r........_ ----