provide for the payment of equal rather than uniformly varying sums. If the interest rate
of the loan was 8 percent, what was the annual payment?
Calculation Procedure:- Apply the equivalent-uniform-series equation
Let R 1 = initial payment in a uniform-gradient series; g = difference between successive
payments; n = number of payments; Re = periodic payment in an equivalent uniform se-
ries. Then R 6 = R 1 + (gli)(\ - «SFP). Substituting with ^ 1 = $5000, g = $400, n = 6, and
i = 8 percent, we find R 6 = $5000 + ($400/0.08)(1 - 6 x 0.13632) = $5911. - As an alternative, use the uniform-gradient conversion
(UGC) factor
With n = 6 and / = 8 percent, UGC = 2.28. Then, Re = $5000 + $400(2.28) = $5912.
PRESENT WORTH OF UNIFORM-GRADIENT
SERIES
Under the terms of a contract, Brown Corp. was to receive a payment at the end of each
year from year 1 to year 7, with the payments varying uniformly from $8000 in year 1 to
$5000 in year 7. At the beginning of year 1, Brown Corp. assigned its annuity to Edwards
Corp. at a price that yielded Edwards Corp. a 6 percent investment rate. What did Ed-
wards Corp. pay for the annuity?
Calculation Procedure:- Apply the relation of step 1 of the previous
calculation procedure
The relation referred to converts a uniform-gradient series to an equivalent uniform se-
ries. Thus, with g = -$500, n = 7, and i = 6 percent, we get Re = $8000 + (-$500/0.06) x
(1-7 x 0.11914) = $6617. - Compute the present worth of the equivalent annuity
Use the relation P = R 6 (USPW) = $6617(5.582) = $36,936.
FUTURE VALUE OF UNIFORM-RATE SERIES
A deposit was made in a fund at the end of each year for 8 consecutive years. The first de-
posit was $1000, and each deposit thereafter was 25 percent more than the preceding de-
posit. If the interest rate of the fund was 7 percent per annum, what was the principal in
the fund immediately after the eighth deposit was made?
Calculation Procedure:- Compute the URSCA value
A uniform-rate series is a set of payments made at equal intervals in which the payments