210 Energy Project Financing: Resources and Strategies for Success
For Simple Interest
Fn = P (1+n*i)Example 3
Determine the balance which will accumulate at the end of year 4 in
an account which pays 10%/yr simple interest if a deposit of $500 is made
today.Fn = P * (1 + n*i)
F 4 = 500 * (1 + 4*0.10)
F 4 = 500 * (1 + 0.40)
F 4 = 500 * (1.40)
F 4 = $700A.6.4 Compound Interest
For compound interest, interest is earned (charged) on the original
principal amount, plus any accumulated interest from previous years at
the rate of i% per year (i%/yr). Table A-5 illustrates the annual calculation
of compound interest. In the Table A-5 and the formulas which follow, i is
expressed as a decimal amount (i.e., 8% interest is expressed as 0.08).
At the beginning of year 1 (end of year 0), P dollars (e.g., $100) are
deposited in an account earning i%/yr (e.g., 8%/yr or 0.08) compound
interest. Under compound interest, during year 1 the P dollars ($100) earn
P*i dollars ($100*0.08 = $8) of interest. Notice that this the same as the
amount earned under simple compounding. This result is expected since
the interest earned in previous years is zero for year 1. At the end of the
year 1 the balance in the account is obtain by adding P dollars (the original
principal, $100) plus P*i (the interest earned during year 1, $8) to obtain
P+P*i ($100+$8 = $108). Through algebraic manipulation, the end of year
1 balance can be expressed mathematically as P*(1+i) dollars ($100*1.08 =
$108).
During year 2 and subsequent years, we begin to see the power (if
you are a lender) or penalty (if you are a borrower) of compound interest
over simple interest. The beginning of year 2 is the same point in time as
the end of year 1 so the balance in the account is P*(1+i) dollars ($108).
During year 2 the account earns i% interest on the original principal, P
dollars ($100), and it earns i% interest on the accumulated interest from
year 1, P*i dollars ($8). Thus the interest earned in year 2 is [P+P*i]*i dol-