Handbook of Civil Engineering Calculations

Compound interest—uniform-payment series: R = sum paid at end of each interest pe-
riod for n periods; P = value of payments at beginning of first interest period, also termed
present worth of payments; S = value of payments at end of nth interest period, also
termed future value of payments.
Compound interest—uniform-gradient series: Rm = payment at end of mth interest pe-
riod; g = constant difference between given payment and preceding payment, also termed
gradient of series. Then Rm = RI + (m— l)g. Also, P and S have the same meaning as for
uniform-payment series.
Compound interest—uniform-rate series: Rm = payment at end of mth interest period;
r = constant ratio of given payment to preceding payment. Then Rm = R^"
1
'
1
, and P and S
have the same meaning as for uniform-payment series.
Compound-interest factors: Single payment—SIP = single-payment compound-
amount (SPCA) factor; PIS = single-payment present-worth (SPPW) factor. Uniform-
payment series—SIR = uniform-series compound-amount (USCA) factor; RfS = sinking-
fund-payment (SFP) factor; PIR = uniform-series present-worth (USPW) factor; RIP =
capital-recovery (CR) factor. Uniform-rate series—S/Ri = uniform-rate-series compound-
amount (URSCA) factor; PIR 1 = uniform-rate-series present-worth (URSPW) factor.

Basic Equations

Simple interest, single payment

S = P(l+ni) (1)

Compound interest with discrete compounding

SPCA = (1 + O" (2)

SPPW = (I+/)"" (3)

USCA-P

+

P-

1

(4)

I

SFP=

(TTTFTT <

5

>

"

8

^-^TTTF

(6)

CRCR '(1 + O" m

-(l+0«-i

(7)

r"-(\ + iy

URSCA = _./ (^8 )

URSPW=^f 1 "^1 (9)

A uniform-payment series that continues indefinitely is termed a perpetuity. For this

case,