# Question: What is the annual rate the investor would need to earn on a retirement investment?

Today’s question. People seem to be finding them easy so will up the ante a bit: At retirement 9 years from now, an investor will have the option of receiving a lump sum of \$400,000 or 20 annual payments of \$40,000 with the first payment made at retirement. What is the annual rate the investor would need to earn on a retirement investment to be indifferent between the two choices?

Moshe Alexander: May be 3,53% p.a.?

David Geof: afraid not

Stephan Heuler: I don’t have a formula of thumb for that. Is there one?I don’t want to run excel…..;-)

Vikas Garg: Texas B II instrument helps

David Geof: ok hint- PV of 400k – 40k with 0 FV and 19 payments of -40k

Lukas Savickas: People seem to like these puzzles. ðŸ˜€

David Geof: Of course we all like a challenge

Stephan Heuler: “What counts is more important than how to count it!” – admittedly quoted from unknown

Michael Wei: Yes 8.92%. Discount each of the future \$40k payment to PV at the time of the retirement, and find the discount rate to get the *sum* of that discounted cash flow to be exactly \$400k.

Michael Wei: This is a useful calculation for those who won the lottery and trying to decide whether to take the lumpsum or the installments!

David Geof: Well done Craig