Page 275 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

This is the same result as before.

Example 9.17

In Example 9.1, an investment plan for retirement was introduced. It involved investing $5000/year for 40
years leading to retirement. The plan then provided $67,468/year for 20 years of retirement income.
a. What yearly interest rate was used in this evaluation?
b. How much money was invested in the retirement plan before withdrawals began?

Solution

a. The evaluation is performed in two steps.
Step 1: Find the value of the $5000 annuity investment at the end of the 40 years.
Step 2: Evaluate the interest rate of an annuity that will pay out this amount in 20 years at $67,468/
year.
Step 1: From Equation (9.11), Table 9.1, for A = $5000 and n = 40,
40
F = (A)(F/A, n, i) = ($5000) [(1+i) – 1]/i
40
Step 2: From Equation (9.14), Table 9.1, for A = $67,468 and n = 20,
20
20
P = (A)(P/A, n, i) = ($67,468)[(1 + i) – 1]/[(i)(1 + i) ]
Set F = P and solve for i. From Figure E9.17, i = 0.060
40

Figure E9.17 Determination of Interest Rate for Example 9.17

b. With i = 0.060, from Figure E9.17, F = $774,000
40

Note: The interest rate of 6.0% p.a. represents a relatively low interest rate, involving small risk.

9.6 Inflation