Page 27 - FINAL CFA I SLIDES JUNE 2019 DAY 2

LOS 6.f: Demonstrate the use of a time line in Session Unit 2: The Time Value of Money
modelling and solving time value of money problems.

Example: Funding a retirement plan: Assume a 35-year-old investor wants to retire in 25 years at the age of 60. She
expects to earn 12.5% on her investments prior to her retirement and 10% thereafter. How much must she deposit at the
end of each year for the next 25 years in order to be able to withdraw $25,000 per year at the beginning of each year for
30 years?

Answer: PV of the $25,000, 30-year annuity due at the beginning of Year 26 (end of Year 25 when he retires!).

END mode (if BGN then N = 30 not 29):
• N = 29; I/Y = 10; PMT = –$25,000;
• CPT → PV = $234,240 (for 29 years)
If you did END mode with N = 30!

• Now, add the first annuity payment to get $234,240 + $25,000 = $259,240. Amount needed at the
end of Year 25 to fund
retirement plans!

Or

• BGN Mode ([2nd] [BGN] [2nd] [SET] [2nd] [QUIT] :
• N = 30; PMT = –25,000; I/Y = 10; So, investor must deposit:
• CPT → PV = 259,240.14

• N = 25; I/Y = 12.5; FV = –259,240;
• CPT → PMT = $1,800.02