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Math Help - Interesting Interest

  1. #1
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    Question Interesting Interest

    Suppose one borrowed $400.00 per month for 54 months at 6 percent. After final $400.00 one waited 3 months and began repayment of loan at $200.00 per month for 72 months, then increased to $600.00 per month until loan was paid off. 1) what would be amount of interest owed before repayment started? 2) What would balance be after 72 months of $200 per month payments? 3) When would loan be paid off and what would total amount be?
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  2. #2
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    Re: Interesting Interest

    Quote Originally Posted by SusanMM View Post
    Suppose one borrowed \$400.00 per month for 54 months at 6 percent. After final $400.00 one waited 3 months and began repayment of loan at \$200.00 per month for 72 months, then increased to \$600.00 per month until loan was paid off. 1) what would be amount of interest owed before repayment started? 2) What would balance be after 72 months of \$200 per month payments? 3) When would loan be paid off and what would total amount be?
    I fixed your question, which belongs in business math. Is your final question what would be the total of the payments or the total in interest paid?

    I can simply give you an answer if you this is a practical problem. if you are a student, however, a simple answer will do you no good when you get to your test. It looks sort of like a class problem so I am guessing you are a student. In that case, do you know the formulas for future and present value of annuities? Can you see how to set this up in excel? Either method will work.

    I suspect it's best to use the formulas because that is what you will have available on a test. If you know the formulas, what's your best guess on how to use them?
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  3. #3
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    Re: Interesting Interest

    Jeff, Thank you, I appreciate your help. I am not a student and this is a practical problem. I would like the answers (both to #3), formulas and how to set up in Excel - if it is not too much. I would like to understand calculations and make adjustments if needed. Susan
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  4. #4
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    Re: Interesting Interest

    Susan

    I do not have time to give a complete exposition of the basic formulas right now: my wife can always find things for me to do. For some of the economic ideas behind the formulas, you might want to look at my answer to this question Present Discounted Value of Payment

    Anyway, the basic formulas are for present value and future value:

    $P = \dfrac{A}{(1 + r)^n}\ and\ F = A(1 + r)^n,$ where

    A = the sum of money involved.
    r = the effective interest rate per period.
    n = the number of periods.
    P = the present value (market value right now) of A units of money to be received n periods from now.
    F = the future value n periods from now of an immediate investment of A units of money.

    Couple of things. Interest rates are usually expressed in terms of years, but interest is usually computed more frequently. A period in these formulas is the period for which interest is computed, and the effective interest rate per period = annual rate divided by the number of computing (compounding) periods per year. So if interest is computed by the month, n is the number of months and r = the annual rate / 12. Notice that P involves the value at the start of the first period of a payment received at the end of the nth period, and F involves the value at the end of the nth period of an investment made at the start of the first period. It is important to keep starting and ending times straight.

    The other two common formulas are the formulas related to a series of equal successive payments (sometimes called an annuity).

    $S = A * \dfrac{1 - (1 - r)^{-n}}{r}\ and\ T = A * \dfrac{(1 + r)^n - 1}{r} * (1 + r),$ where

    S = the present value at the start of the first period of n payments of A each made at the end of n successive periods, starting with the first period
    T = the future value at the end of the nth period of n payments of A each made at the start of n successive periods, starting with the first period.

    Combining those four formulas appropriately will usually allow you to deal with just about any series of cash flows.

    Now some of these formulas are built into excel, but excel will not tell you how to use them properly. If you are skilled with a scientific calculator and algebra, you can ignore excel and just use the formulas on your calculator. Otherwise (or if you need to explain your results), excel is excellent, but don't rely exclusively on the built-in the formulas. Always do the basic arithmetic using copy and paste whether or not you use the formulas: you will catch mistakes that way and everyone will understand what you did.

    If you want to send me your email address by private message, I can send you an excel spread sheet that deals with your specific problem as well as shows you the formulas in use. I can't promise you when you will get your answer; I do have other things to do. It may take a day or so. Anyway, I suspect you will learn from this problem how to use excel for more general problems of this type.
    Last edited by JeffM; April 13th 2014 at 10:41 AM.
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  5. #5
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    Re: Interesting Interest

    Thank you so much Jeff, I will work / play with the equations to see what I can do. I'll let you know how it goes. Also thank your wife for sharing your time helping me with this!!!
    Susan
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  6. #6
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    Re: Interesting Interest

    Hello Susan,
    Using the compound amount Factor F= (1+i)^n-1/i
    S=R*F S is sumof values of R investments for n terms at term interest
    when n=54,i=0.005 and R =$400 F =1.309-1/0.005 =61.82
    S =400*61.82 =$24728 the debt of borrower after his receipt of last $400 payment
    When repayment is delayed 3 months this value increases by (1+i)^3
    Use same CAF for repayment changing n,R as needed
    I calculate that the debt of borrower would be paid after 142 months.Last payment $ 410
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  7. #7
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    Re: Interesting Interest

    The bottom two lines of my post 6 somehow got mixed up.After the borrower gets his last $ 400 loan his debt is $ 24728.When repayment is delayed 3 months the amount increases (1+i)^3 times.Use the CAF formula to calculate repayments changing n and R as needed.I calculate that the debt would be repaid in 142 months. the last payment is $ 410
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