Energy Project Financing : Resources and Strategies for Success

212 Energy Project Financing: Resources and Strategies for Success

lars ([$100+$8]*0.08 = $8.64). The balance at the end of year 2 is obtained

by adding P dollars (the original principal) plus P*i (the interest from year

1) plus [P+P*i]*i (the interest from year 2) to obtain P+P*i+[P+P*i]*i dollars

($100+$8+$8.64 = $116.64). After some algebraic manipulation, this can

be conveniently written mathematically as P*(1+i)n dollars ($100*1.082 =

$116.64).

Table A-5 extends the above logic to year 3 and then generalizes

the approach for year n. If we return our attention to our original goal of

developing a formula for Fn that is expressed only in terms of the present

amount P, the annual interest rate i, and the number of years n, the above

development and Table A-5 results can be summarized as follows:

For Compound Interest

Fn = P (1+i)n

Example 4

Repeat Example 3 using compound interest rather than simple in-

terest.

Fn = P * (1 + i)n

F 4 = 500 * (1 + 0.10)^4

F 4 = 500 * (1.10)^4

F 4 = 500 * (1.4641)

F 4 = $732.05

Notice that the balance available for withdrawal is higher under

compound interest ($732.05 > $700.00). This is due to earning interest on

principal plus interest rather than earning interest on just original prin-

cipal. Since compound interest is by far more common in practice than

simple interest, the remainder of this appendix is based on compound in-

terest unless explicitly stated otherwise.

A.6.5 Single Sum Cash Flows

Time value of money problems involving compound interest are com-

mon. Because of this frequent need, tables of compound interest time value

of money factors can be found in most books and reference manuals that

deal with economic analysis. The factor (1+i)n is known as the single sum,

future worth factor, or the single payment, compound amount factor. This factor

is denoted (F|P,i,n), where F denotes a future amount, P denotes a present