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# How do I determine the interest rate received on annual payments?

Topic closed. 34 replies. Last post 9 years ago by time*treat.

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San Diego, CA
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 Posted: March 4, 2008, 4:13 pm - IP Logged

If the annual payments total \$9 million over 26 years and the lump sum is \$5.3 million, how do I determine the interest rate received?

San Diego, CA
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 Posted: March 7, 2008, 6:29 pm - IP Logged

(bump).  Does anyone have any insight on this?  The quesion might need clarrification.

If the annual payments total \$9 million over 26 years and the lump sum is \$5.3 million, how do I determine the interest rate received if I take the annjual payments.

Wandering Aimlessly
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 Posted: March 7, 2008, 6:40 pm - IP Logged

Depends what you mean. If you take \$9M and divide by 26 you get about \$346K a year. So the rate on \$9M each year would be is 3.85% since 9,000,000 x 3.85% = \$346,500

If you took the lump sum, your interest rate would vary depending on your investments.  Averaging 6% a year for 12 years doubles your money.   Investing in stocks, commodities, real estate, etc. should increase that amount substantially, but there is always some risk.

Zeta Reticuli Star System
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 Posted: March 7, 2008, 7:14 pm - IP Logged

I think he's asking for the difference between the annuity and the cash option, if he was to get interest on both amounts from the get go, and then compare them.

Since the annuity amount does not exaist as a lump sum, I don't think there can be an answer.

Those who run the lotteries love it when players look for consistency in something that's designed not to have any.

There is one and only one 'proven' system, and that is to book the action. No matter the game, let the players pick their own losers.

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 Posted: March 7, 2008, 7:37 pm - IP Logged

If the annual payments total \$9 million over 26 years and the lump sum is \$5.3 million, how do I determine the interest rate received?

If you wanted to start with 5.3 mil and end up with 9 mil after 26 years, you'd need to earn about 2% per year, compounded.

You can find the relevant equations on  the web.

In neo-conned Amerika, bank robs you.
Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

San Diego, CA
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 Posted: March 7, 2008, 8:12 pm - IP Logged

If you wanted to start with 5.3 mil and end up with 9 mil after 26 years, you'd need to earn about 2% per year, compounded.

You can find the relevant equations on  the web.

Yes that is what I am looking for. Where can I find the equation?

Wandering Aimlessly
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 Posted: March 7, 2008, 8:21 pm - IP Logged

I obviously misunderstood the question. I guess I didn't even consider it since nobody would invest the entire lump sum in an interest bearing account.  What would be the point?  Usually someone wants to enjoy at least a portion of his/her prize. I'm guessing most people would purchase a nicer home (and probably a vacation home too) and buy a couple of new cars.  So, although it's not hard to figure the interest over 26 years, it's not what would happen in the real world.

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 Posted: March 7, 2008, 8:36 pm - IP Logged

Yes that is what I am looking for. Where can I find the equation?

if you want all the grimy details: http://en.wikipedia.org/wiki/Compound_interest

if you just want to get some work done: http://moneychimp.com/calculator/discount_rate_calculator.htm

In neo-conned Amerika, bank robs you.
Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

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 Posted: March 7, 2008, 11:20 pm - IP Logged

Judging from the performance of the dollar you would be insane to choose the annuity a lottery offers now. Far better to choose a fund that has global diversity along with some gold or other comodities.

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 Posted: March 7, 2008, 11:22 pm - IP Logged

Judging from the performance of the dollar you would be insane to choose the annuity a lottery offers now. Far better to choose a fund that has global diversity along with some gold or other comodities.

Hey! That's my line.

In neo-conned Amerika, bank robs you.
Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

Wandering Aimlessly
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 Posted: March 8, 2008, 12:31 am - IP Logged

Hey! That's my line.

Which is why I said "Investing in stocks, commodities, real estate, etc." and didn't get specific.   I knew you'd write that!

New Member
Fayetteville, Arkansas
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 Posted: March 8, 2008, 2:25 am - IP Logged

If the annual payments total \$9 million over 26 years and the lump sum is \$5.3 million, how do I determine the interest rate received?

The formula which shows the basic relationship is not hard to find; but solving for the interest rate ... that's another matter.

I love problems of this kind; but in this case the math is way beyond me.

Accountants interpolate from a table to solve this problem, and you can set up a spreadsheet with an incremental series of values and interpolate to get an approximation.

(1)  PV = A * (((1 - ((1 + i)^(-n))) / i)

where PV = present value of the annuity, A = amount of payment, i = interest rate, n = number of payments.

(2)  i = R - (R * ((1 + i)^(-n)))

where R = A / PV

Incidently, if you're talking about MegaMillions, I think n = 27, not 26; don't forget that first payment, which you get immediately.

The balls have no memory.

San Diego, CA
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 Posted: March 8, 2008, 11:07 am - IP Logged

The formula which shows the basic relationship is not hard to find; but solving for the interest rate ... that's another matter.

I love problems of this kind; but in this case the math is way beyond me.

Accountants interpolate from a table to solve this problem, and you can set up a spreadsheet with an incremental series of values and interpolate to get an approximation.

(1)  PV = A * (((1 - ((1 + i)^(-n))) / i)

where PV = present value of the annuity, A = amount of payment, i = interest rate, n = number of payments.

(2)  i = R - (R * ((1 + i)^(-n)))

where R = A / PV

Incidently, if you're talking about MegaMillions, I think n = 27, not 26; don't forget that first payment, which you get immediately.

I thought it was going to be basic, but determined it would be complex considering money is being paid out in the annual installments.  What complicates things further is the payment percentage usually changes every year.

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 Posted: March 8, 2008, 11:13 am - IP Logged

It's mainly a matter of deciding which number you want constant.

If you hold the interest rate constant, the nominal payout amount changes.

If you hold the nominal payout amount constant, then the interest rate is changing.

In neo-conned Amerika, bank robs you.
Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

NY
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 Posted: March 8, 2008, 11:34 am - IP Logged

It works exactly like any other loan. They owe you 5.3 million now, but they pay it to you in annual installments of \$346,154 totalling \$9 million. After the first payment they still owe you about \$5 million. A rate of 4.66% compounded monthly would repay the remainder in annual installments of \$346,310, which is close enough.  A payment that increases each year definitely complicates the math. They already know the interest rate and do a simple amortization table. Working backwards to figure out what the rate is a collossal PITA, and require a program, and not ust asimple loan calculator. There are two other things you may also want to consider.

1. Why does it matter what the interest rate is when you know exaclty what the actual payment will be?
2. You will be earning that 4.66% interest on the  35 to 42% that  you would lose to taxes if you choose the lump sum. To earn 346k on the \$3.445 million you'd have after paying federal taxes you'd need to earn 10% interest.

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