

Subject:
calculating payment amount for annuity
Category: Business and Money > Finance Asked by: chrisnga List Price: $5.00 
Posted:
23 Oct 2003 13:09 PDT
Expires: 22 Nov 2003 12:09 PST Question ID: 269131 
A person wishes to have $992354.70 after 40 years with 7% interest compounded annually. I believe this is done by taking the present value of an annuity. If this is correct, please explain how this is done mathematically (IE not using a financial calculator and not referring to tables for needed values). If not, please explain the process keeping the above in mind. Please include necessary equations and work through them to show the process. If fractions are used, write them using parentheses rather than vertically. Feel free to ask for clarification if you need more information to be able to provide a helpful answer. Thanks..  
 


Subject:
Re: calculating payment amount for annuity
Answered By: answerguruga on 23 Oct 2003 16:15 PDT Rated: 
Hi chrisnga, Here is your question again: A person wishes to have $992354.70 after 40 years with 7% interest compounded annually. He needs to make equal payments each year. Here is how you solve this type of problem: This is a present value annuity problem  these types of annuities are solved using the following formula: PV annuity = C*((1  (1/(1+r)^t))/r) where: C = Periodic cash payments r = interest rate t = number of periods You are already given the PV annuity value, interest rate, and number of periods, so we can solve for C: $992354.70 = C*((1  (1/(1+0.07)^40))/0.07) C = $992354.70 / ((1  (1/(1+0.07)^40))/0.07) = $992354.70 / (0.9332/0.07) = $992354.70 / 13.332 = $74435.67 So this person will need to make annual payments of $$74435.67 in order to have the desired amount in 40 years given an interest rate of 7%. Hopefully this helps you understand the calculation behind this value. If you have any problems understanding the information above please let me know :) Cheers! answerguruga 
chrisnga
rated this answer:
Thank you. That is exactly what I was looking for. 

Subject:
Re: calculating payment amount for annuity
From: respreega on 23 Oct 2003 20:25 PDT 
I'm not a math whiz, but you might want to check the math again. If you saved $74,435.67 for 40 years with 'no' interest, thats $2.97 million. Did I miss something? 
Subject:
Re: calculating payment amount for annuity
From: chrisnga on 24 Oct 2003 05:51 PDT 
Yeah. The format, as far as how the information was presented, is great. Something with the formula itself doesn't appear correct. Consider this a request for clarification if you should come across this question...otherwise it's my own fault for not checking the results fully before closing the question. 
Subject:
Re: calculating payment amount for annuity
From: respreega on 24 Oct 2003 10:11 PDT 
You may want to try this online tool: http://www.localok.com/savecalc.html 
Subject:
Re: calculating payment amount for annuity
From: answerguruga on 24 Oct 2003 15:12 PDT 
OK, I'm am feeling quite sheepish :) I saw your mention of present value annuity in the question and assumed that is what you wanted the calculation for  what you actually need is the FUTURE value annuity. The question answered in the orginal question was "how much should I pay for an investment that gives an annual payment of 7% for the next 40 years". This is the inverse of the question you actually wanted answered. OK, so now for the future value annuity calculation: FV annuity = C*(((1+r)^t  1)/r) C = FV annuity / (((1+r)^t  1)/r) = $992354.70 / 199.635112 = $4970.84 Hopefully that dissolves all the confusion :) answerguruga 
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