Handbook of Civil Engineering Calculations

USPW = - (6a)

CR = / (7a)

Compound interest with continuous compounding

SPCA = eJ" (10)

where e = base of natural logarithms = 2.71828 ...

SPPW = IT'^11 (11)

USCA

=7rff

(12)

\-e~jn

USPW= * (13)

e^7 — 1

The compound-interest factors for a single payment and for a uniform-payment series
can be found by referring to compound-interest tables or by solving the relevant equations
by calculator.

DETERMINATION OF SIMPLE INTEREST

A company borrows $4000 at 6 percent per annum simple interest. What payment must
be made to retire the debt at the end of 5 years?

Calculation Procedure:

Apply the equation for simple interest

This equation is S = P(I + ni) = $4000(1 + 5 x 0.06) = $5200.

Note: See the introduction to this section for the symbols used.

COMPOUND INTEREST; FUTURE VALUE OF

SINGLEPAYMENT

The sum of $2600 was deposited in a fund that earned interest at 8 percent per annum

compounded quarterly. What was the principal in the fund at the end of 3 years?

Calculation Procedure:

1. Compute the true interest rate and number of interest periods
   Since there are four interest periods per year, the interest rate i per period is i = 8 per-
   cent/4 = 2 percent per period. With a 3-year deposit period, the number n of interest peri-
   ods is n = 3 x 4 - 12.