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Math Help - Another similar problem.

  1. #1
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    Another similar problem.

    Sorry, I just found another difficult problem. It deals with RAM and I used to wikipedia to find out what that means, since my book does not cover this.

    Sinclair wishes to supplement his retirement income by $450 per month for the next
    15 years. He plans to obtain a reverse annuity mortgage (RAM) on his home to meet
    this need. Estimate the amount of themortgage he will require if the prevailing interest
    rate is 11% per year compounded continuously. Round your answer to the nearest dollar

    Does anyone know how to work with RAM?
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  2. #2
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    Quote Originally Posted by rmr62353 View Post
    Sorry, I just found another difficult problem. It deals with RAM and I used to wikipedia to find out what that means, since my book does not cover this.

    Sinclair wishes to supplement his retirement income by $450 per month for the next
    15 years. He plans to obtain a reverse annuity mortgage (RAM) on his home to meet
    this need. Estimate the amount of themortgage he will require if the prevailing interest
    rate is 11% per year compounded continuously. Round your answer to the nearest dollar

    Does anyone know how to work with RAM?
    I think the RAM is just filler in this problem. What you want is the PV of a continous annuity with 450 for a payment, (15*12 = 180) for n, and 11% for interest.

    I know there is some discord on the formula. I personally stand by Kellison's formula, but you can go here as well:

    Time value of money - Wikipedia, the free encyclopedia
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  3. #3
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    Thanks for the insight. I'm still not sure which formula to use..? I looked at the links..I'm still kind of confused.
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  4. #4
    Member jonah's Avatar
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    I think you should use the formula indicated by
    (5.1 Present value of an annuity) → PV = A[1-e^(-rt)]/[e^r-1)
    Unfortunately, there seems to be a typo with this formula.
    Using the same notation I used on your first thread, the answer to your problem might be

    A = R(1 – e^[-jt])/(e^[j/m]-1) = $39,481.49

    A” = R + R(1 – e^[-j(tm-1)/m])/(e^[j/m]-1) = $39,845.07
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  5. #5
    Member jonah's Avatar
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    My apologies to the author of the formula for the present value of an annuity where the interest compounding is continuous as posted in the Wikipedia entry for the Time value of money for insinuating that there may have been a typo with that formula. Drowsiness caused me to commit a typo myself by posting PV = A[1-e^(-rt)]/[e^r-1 instead of PV = A[1-e^(-rt)]/[e^r-1]. Drowsiness also caused me to think that the formula itself was lacking a certain element when I tested it for the problem concerning Sinclair. Subsequent subconscious assimilation tells me that PV = A[1-e^(-rt)]/[e^r-1] is the special case of the first formula I came up with where the periodic payment is annually. It would seem that the first formula for the present value of an (ordinary) annuity that I posted is the general case where m may be annually, semi-annually, quarterly, monthly, semi-monthly, weekly, etc. Many thanks to you rmr62353 for posting this problem and to your professor for coming up with such two unusual problems.

    Advertising aside, authors William L. Hart (Mathematics of Investment, fifth edition, ca 1975), Ronald J. Harshbarger & James J. Reynolds (Mathematical Applications for management, life and social sciences, second edition, ca 1985), Stephen P. Shao & Lawrence P. Shao (Mathematics for management and finance, eighth edition, ca 1998), and lately, Terry J. Watsham & Keith Parramore (Quantitative Methods in Finance, First Edition, ca 1997, where the formula for converting a continuously compounded rate to a discretely compounded equivalent rate & vice versa was explicitly stated), and other authors I’ve come across have all mentioned and treated continuous compounding to a certain extent, but the two problems that you posted is the first time I ever encountered an “actual” continuous compounding application in annuities. Most textbook exercises on continuous compounding I’ve seen are about compound interest and conversion exercises. I hope its not too much trouble but would you mind mentioning the name and author of the textbook where your teacher lifted the two problems that you posted – assuming of course that those problems were lifted from a textbook. I would indeed be very much interested in adding it to my source of references.

    P.S. Would any bank seriously consider granting Sinclair’s mortgage/loan application considering his retired status? Perhaps Sinclair’s home is enough security? I’m confused. At any rate, attached with this post are four excel amortization schedules. Two are ordinary and two are annuity due.
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  6. #6
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    Jonah thank you so much for all the information. my teacher did not use the math text for these problems..i could not find a similar example. she either made them up or used another source. the book is called: Calculus for the Managerial, Life, and Social Sciences.

    I'm dealing with annuities in my financial accounting class, and we use tables to figure out the values we need in order to calculate present value and future value of 1 or of an annuity. so I guess i was just looking for a straight forward formula in this case, but this was a bonus question assigned for extra credit. i appreciate the long reply on your part.
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