FUTURE VALUE OF UNIFORM SERIES
WITH CONTINUOUS COMPOUNDING
An inventor received a royalty payment of $25,000 at the end of each year for 7 years.
The royalties were invested at 12 percent per annum compounded continuously. What
was the inventor's capital at the expiration of the 7-year period?
Calculation Procedure:- Compute the USCA value
Apply Eq. 12: USCA - (e
jn
- V)I(e
f - 1), where n - number of annual payments in uni-
form-payment series and e and j are as defined in the previous calculation procedure.
Thus, with /i = 7 andy = 12 percent, USCA = (e
0
84
- l)/(e°-
12
- = 10.325.
- Compute the future value of the series
Set S = ,R(USCA) = $25,000(10.325) = $258,100.
Related Calculations: Note that if interest were compounded annually at 12 per-
cent, the USCA value would be 10.089.
PRESENT WORTH OF CONTINUOUS CASH
FLOW OF UNIFORM RATE
An investment syndicate is contemplating purchase of a business that is expected to yield
an income of $200,000 per year continuously and at a constant rate for the next 5 years. If
the syndicate wishes to earn 18 percent on its investment, what is the maximum price it
should offer for the business?
Calculation Procedure:- Compute the present-worth factor
Apply the equation CFPW = (1 - e~Jn)/j, where CFPW = present-worth factor for a contin-
uous cash flow of uniform rate and n = number of years of the flow. Where the cash flow
is continuous, it is understood that the given interest or investment rate is based on contin-
uous compounding. Thus, with n = 5 and 7 = 18 percent, CFPW = (1 - £T°-^90 )/0.18 =
3.297. - Compute the present worth of the income
Set P = jR(CFPW), where R = annual cash-flow rate. Then P = $200,000(3.297) =
$659,400.
FUTURE VALUE OF CONTINUOUS CASH
FLOWOFUNIFORMRATE
The sum of $30 will be invested daily in a venture that yields 14 percent per annum. What
will be the accumulated capital at the expiration of 18 months?