Page 273 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

P = $1,019,000

A present value of $1,019,000 is equivalent to a 20-year annuity of $100,000/yr when the effective
interest rate is 9.5%.

Examples 9.15 through 9.17 illustrate how to use these discount factors and how to approach problems
involving discrete CFDs.

Example 9.15

Consider Example 9.11, involving a car loan. The discrete CFD from the bank’s point of view was
shown.

What interest rate is the bank charging for this loan?

You have agreed to make 36 monthly payments of $320. The time selected for evaluation is the time at
which the final payment is made. At this time, the loan will be fully paid off. This means that the future
value of the $10,000 borrowed is equivalent to a $320 annuity over 36 payments.

($10,000)(F/P, i, n) = ($320)(F/A, i, n)

Substituting the equations for the discount factors given in Table 9.1, with n = 36 months, yields

36
36
0 = –(10,000)(1 + i) + (320)[(1 + i) –1]/i
This equation cannot be solved explicitly for i. It is solved by plotting the value of the right-hand side of
the equation shown above for various interest rates. This equation could also be solved using a numerical
technique. From Figure E9.15, the interest rate that gives a value of zero represents the answer. From
Figure E9.15 the rate of interest is i = 0.0079.

Figure E9.15 Determination of Interest Rate for Example 9.15

The nominal annual interest rate is (12)(0.00786) = 0.095 (9.5%).