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February 13th, 2017, 06:59 PM   #1
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How to solve for monthly amount to get $200k payout after specific payment term?

I am trying to find a formula to solve for the monthly starting amount below:

Monthly Starting Amount = ?
Payment Term = 10 years, 5 months (125 monthly payments)
Indexation = 2% per year, compounded
Total Future Payout = \$200,000.00

That is, what is the required monthly starting amount you must invest if you want a payout of \$200,000.00 after 125 monthly payments, if payments increase by 2% per year, compounded?

I know the answer is \$1,454.63 with \$0.45 remaining at the end of the term, but I am not sure how to get there. Any help would be appreciated.

I also know that without indexation, it's simply \$1,600.00 (\$200,000.00 / 125).

Last edited by skipjack; February 13th, 2017 at 07:04 PM.
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February 13th, 2017, 07:10 PM   #2
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If you made only one payment, how much would it become after 125 months?
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February 13th, 2017, 07:51 PM   #3
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I am not sure how I would answer that without knowing what the monthly payment is?
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February 13th, 2017, 07:51 PM   #4
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The question simply cannot be answered as given. Furthermore, the obvious ways to fill in the problem lead to a non-standard and very complex formula. The basic issue is that the given compounding period does not divide evenly into the period of investment.

If I make a payment on March 1, 2017, does that payment receive an interest credit on March 1, 2018, or January 1, 2018? If March, what happens with respect to a payment made on April 1, 2017. Does it too receive an interest credit on March 1, 2018. If so, how is that interest credit for only 11 months calculated.

If interest was being compounded monthly and so coincided with monthly payments, the standard formula available in basic finance texts could be used, but that does not seem to be the question being asked.
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February 13th, 2017, 08:03 PM   #5
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Just to clarify, there is no mathematical equation I can use to solve for the starting monthly amount (disregarding the remaining amount at the end of the term)?

I work in the insurance industry and my company has a program where I can enter a monthly amount (along with the annual indexation rate and total desired payout) and it solves for the payment term. However, when I want the payment term to be a specific period (i.e., 10 years and 5 months), it requires trial and error to determine the monthly amount. For example, I keep entering monthly amounts until I get the payment term I desire. Is there any way around this?
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February 13th, 2017, 08:18 PM   #6
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I shall try to give you a formula (or an algorithm) if you answer the questions I have posed. How is interest computed when payments are monthly, but compounding is annual? How do you deal with stub periods, etc?

Some problems in financial mathmatics do not have a closed form formula, but can be solved by numerical methods relatively easily.
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February 13th, 2017, 08:37 PM   #7
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I'll try to answer your question. I have not really used much math since I graduated from university years ago (and even then it was never my strong suit) so please bare with me.

The program I use at work does not show any work (so I am not sure how it even calculates the payment term), but it is my understanding that it assumes the monthly amount increases on the start date.

For example:

If I am using a monthly amount of 100.00, commencing on March 1, 2017, the monthly amount would increase to 100.20 on March 1, 2018.

So for the first 12 months it would generate a monthly amount of 100.00, and the next 12 months would generate 100.20 per month.

I notice you are using the term interest. Are interest and inflation calculated the same way?

(Sorry if the formatting is weird - this website is not working very well with my BlackBerry for some reason.)

Last edited by mshaughn; February 13th, 2017 at 08:47 PM.
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February 13th, 2017, 09:13 PM   #8
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It's late here. So this will be my last post until tomorrow.

If you give someone 100.00 on March 1, 2017 and they owe you 100.20 on March 1, 2018, then whether you call it indexation or an interest accrual is just different terminology although in any terminology it is 0.2% rather than 2%. (The difference in terminology may have legal ramifications in Canada; my only familiarity with Canadian financial law is with the rather odd rules for clearing checks among Canadian banks when the checks are denominated in US dollars. Anything have to do with Canadian financial law will have to wait for mon ami denis.)

And yes, the math of inflation or any other rate of increase is the same as the math of interest (which is just the rate of increase in money.)

I am sorry if I have not been clear. My problem here is that you seem to be talking about payments made monthly for 125 months, but interest or indexation compounded annually (every 12 months). One way to proceed is to assume simple interest for fractions of years up until some anniversary date (after which annual adjustments are made to what has been accumulated so far) and a stub period of 5 months with simple interest at the end. Unless I know how this contract is supposed to work when payments and compounding are persistently out of phase, the problem is not well specified.

If this were a contract in the US, it might well be in violation of the Truth in Savings Act if it did not provide standardized disclosures. As described, it is very peculiar.
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February 13th, 2017, 09:24 PM   #9
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It occurs to me that you are trying to set up some sort of financial plan for yourself or someone else. If that is the case, why don't you explain what you are trying to do in plain English without any technical terms like compounding or indexation.
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February 13th, 2017, 09:48 PM   #10
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Quote:
Originally Posted by mshaughn View Post
I am not sure how I would answer that without knowing what the monthly payment is?
It doesn't matter much, as I just wanted to know precisely how the indexation is done. Use \$1000 if you like.
Thanks from JeffM1 and mshaughn
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