Economics Appendix E Homework Inflation 300 Initial Sum 1000000 Years 1

Appendix 5B Growing Annuities

Answers and Solutions

5B-1

Web Appendix 5B

Growing Annuities

Answers to Questions

5B-1 An annuity is defined as a series of constant payments to be received over a specified number of

periods. The term growing annuity is used to describe a series of payments that are growing at a

5B-2 Growing annuity problems can be solved two ways: (1) Calculator approach and (2) Spreadsheet

model. If you use a financial calculator, first calculate the real rate of return, which is the nominal

rate adjusted for inflation, and then use it for I to find the initial payment.

Solutions to Problems

5B-2 rNOM = 5.00%; Inflation = 2.50%

rr = [(1 + rNOM)/(1 + Inflation)] – 1

5B-3 rNOM = 9.00%; Inflation = 3.00%; Initial sum = $1,000,000; Years = 20

Begin Mode:

N 20

5B-4 rNOM = 9.00%; Inflation = 3.00%; Initial sum = $1,000,000; Years = 20

End Mode:

N 20

I/YR 5.825243

Appendix 5B Growing Annuities

Answers and Solutions

5B-3

5B-5 Step 1. Calculate the purchasing power of $1,500,000 in 30 years at an inflation rate of 4%:

N 30

I/YR 4.0

Step 2. Calculate the real rate of return on the growing annuity:

rNOM = 6.0%; Growth = 4.0%

Step 3. Calculate the required initial payment of the growing annuity by using inputs converted

to “real” terms:

Begin Mode:

5B-6 Step 1. Calculate the purchasing power of $2,500,000 in 35 years at an inflation rate of 2%:

N 35

I/YR 2.0

Step 2. Calculate the real rate of return on the growing annuity:

rNOM = 9.0%; Inflation = 2.0%

Step 3. Calculate the required initial payment of the growing annuity by using inputs converted

to “real” terms: