Determining Correct Years of Growth

Course 1: Fundamentals of Financial Planning
Lesson 5: Using the Calculator

Student Question:

Hello, in the question below, I am a little lost on why it is 9 years for N instead of 10?  Could you explain?

In Year 1, Harvey assumed he would need the equivalent of $500,000 in Year 1 dollars to retire in Year 10. He assumed he could earn 7% after-tax and that inflation would grow at a 9% rate. He will need retirement income beginning on the first day of January of each year during his retirement. What did Harvey need to set aside at the end of each year to reach his objective in Year 10? Round your answer to the nearest cent.

$74,832.51
$80,854.21
$86,915.42
$90,661.85

Remember, this is a two-part question. There is no cash flow except for the payments that are in the “accumulation phase;” thus, you will not use an inflation-adjusted rate.

Solution Keystrokes:

Part 1:
f CLX
g 7
500,000 CHS PV
9 i
9 n
FV

This adjusts Harvey’s need for capital in today’s dollars of $500,000 to $1,085,946.64 after 9 years of inflation.

Part 2:
f CLX
g 8
FV 1,085,946.64
7 i
9 n
PMT

Annual year-end contribution required to grow to specified amount at 7% in 9 years = $90,661.85

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Instructor Response:

Definitely one of those confusing questions.  The reason it’s 9 is because he is setting the money aside at the end of each year, and then would need it at the beginning of year 10.  Therefore, he’s not getting any growth in year 10.

Does that help clarify?