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Math Help - Present Value, Future Value, Rate

  1. #1
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    Unhappy Present Value, Future Value, Rate

    Hello. I am having a hard time determining which function I should be using to solve these problems. Can someone please put me on the right track????? Thanks to anyone that can help me.

    Problem 1: Joe won a lottery jackpot that will pay him $12,000 each year for the next ten years. The market rate is currently 12%. How much does the lottery have to invest today to pay out this prize to Joe over the next ten years?

    Problem 2: Mary just deposited $33,000 in an account paying 10% interest. She plans to leave the money in this account for seven years. How much will she have in her account at the end of the seventh year?

    Problem 3: Mary and Joe would like to save up $10,000 by the end of three years from now. They currently have $2500 in a savings account. They would like to make equal year end deposits to this savings account to pay for furniture when they purchase it three years from now. This account pays 8% interest. How much should the year end payments be?
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  2. #2
    Bar0n janvdl's Avatar
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    Problem 2: Mary just deposited $33,000 in an account paying 10% interest. She plans to leave the money in this account for seven years. How much will she have in her account at the end of the seventh year?
     A = P(1 + \frac{i}{100})^n

     A = (33 000)(1 + \frac{10}{100})^7

     A = 64 308
    Last edited by janvdl; June 5th 2007 at 10:34 AM.
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  3. #3
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    Hello, fw_mathis!

    Here are the first two . . .

    I must assume you are familiar with all the necessary formulas:
    . . compound interest, annuities, amortization, etc.


    1) Joe won a lottery jackpot that will pay him $12,000 a year for the next 10 years.
    The market rate is currently 12%. .How much does the lottery have to invest today
    to pay out this prize to Joe over the next ten years?

    The amortization formula is: . A \:=\:P\frac{i(1+i)^n}{(1+i)^n-1} \quad\Rightarrow\quad P \;=\;A\frac{(1+i)^n - 1}{i(1+i)^n}

    . . where: . \begin{array}{ccc}A & = & \text{periodic payment} \\ P & = & \text{principal invested} \\ i & = & \text{periodic interest rate} \\ n & = & \text{number of periods} \end{array}

    So we have: . P \;=\;12,\!000\!\cdot\!\frac{(1.12)^{10} - 1}{0.12(1.12)^{10}} \;\approx\;\$67,802.68



    2) Mary just deposited $33,000 in an account paying 10% interest.
    She plans to leave the money in this account for seven years.
    How much will she have in her account at the end of the seventh year?
    This is just compound interest: . A \;=\;P(1 + i)^n


    We have: . P = 33,\!000,\:i = 0.10,\:n = 7

    Therefore: . A \;=\;33,\!000(1.10)^7 \;\approx\;\$64,307.66

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  4. #4
    Bar0n janvdl's Avatar
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    I messed up on that first one, thanks Soroban
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  5. #5
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    I need helppppppppppp

    if a person was indebted for $200 that was due after six months & $300 due after one year. if the lender approved of an 18% interst rate per year.Calculate the amount the borrower should pay now.
    if the borrower decided to pay both of the amounts after one year from now. calculate the amount he should pat in that date
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  6. #6
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    PLzzzzzzzz i neeed helpppppp

    Hi ,plz i need ur help .i have an exam after couple of hours.

    if a person was indebeted for $200 that was due after six months & $300 due after one year. if the lender approved of an 18% interst rate per year.Calculate the amount the borrower should ppay now.
    if the borrower decided to pay both of the amounts after one year from now. calculate the amount he should pat in that date

    plz help me soroban...
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by neverlosehope View Post
    Hi ,plz i need ur help .i have an exam after couple of hours.

    if a person was indebeted for $200 that was due after six months & $300 due after one year. if the lender approved of an 18% interst rate per year.Calculate the amount the borrower should ppay now.
    if the borrower decided to pay both of the amounts after one year from now. calculate the amount he should pat in that date

    plz help me soroban...
    your question seems to have information missing, or is at least, not phrased correctly. Please use the exact wording of the question

    Also, please post new questions in a new thread, it's harder for your post to get noticed attaching it to someone else's thread
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  8. #8
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    yes ur right

    sorry yeah there is somthing wrong one min
    it's not that one
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  9. #9
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    help me

    If a person borrowed $2000 at 15%on the first of June 2000 to pay it in two equal times: the first on December 1st, 2000 & the other on June 1st,2001 & if the datum date was June 1st,2000. Calculate the value of each payment
    if the datum date was changed to be 1/6/2001.calculate the value of each payment.

    Using the rule

    p= m/(1+rt)[
    or M= p(1+rt

    Last edited by neverlosehope; June 16th 2007 at 01:30 PM. Reason: wrong speling
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  10. #10
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by neverlosehope View Post
    [FONT='Verdana','sans-serif']If a person borrowed $2000 at 15%on the first of June 2000 to pay it in two equal times: the first on December 1st, 2000 & the other on June 1st,2001 & if the datum date was June 1st,2000. Calculate the value of each payment.[/font][FONT='Verdana','sans-serif']




    Using the rule
    p= m/(1+rt)

    or M= p(1+rt)[/font]
    the interest is applied once every 6 months. he has 1 year to pay it off. so that's two 6 month periods, so the interest would be applied twice. thereofre, t = 2 over all. but we want each payment, so we take t = 1, for the first payment, and t = 1 for the second as well. the rate r, is the percentage written as a decimal, so r = 15% = 0.15. p is the principal, which is the original amount, so p = 1000 (since we have 2 equal installments. M is the amount owed after the said period. so just plug these into the formula.

    Both payents would be the same, so let's just find the first:

    M_1 = p( 1 + rt)

    \Rightarrow M_1 = 1000(1 + (0.15)(1))

    \Rightarrow M_1 = 1150

    So the two payments are:

    M_1 = M_2 = 1150

    if the datum date was changed to be 1/6/2001.calculate the value of each payment.
    the phrase "datum date" is unfamiliar to me, but i suppose it just means that the interest is applied after the year is up.

    we would use r = 0.15, t = 1/2, p = 1000 for each payment, in the same formula. we would get each payment to be 1075
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  11. #11
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    help me

    i have the anser but i don't understand it
    X=1111.24

    & the second part of the question X=11o8.23
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  12. #12
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by neverlosehope View Post
    i have the anser but i don't understand it
    X=1111.24

    & the second part of the question X=11o8.23
    i dont see how those can be the answer either
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  13. #13
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    [FONT='Times New Roman','serif']If a person borrowed $2000 at 15%on the first of June 2000 to pay it in two equal times: the first on December 1st, 2000 & the other on June 1st,2001 & if the datum date was June 1st,2000. Calculate the value of each payment[/FONT][FONT='Times New Roman','serif'][/FONT]
    [FONT='Times New Roman','serif']X??[/FONT]
    [FONT='Times New Roman','serif']p= m/(1+rt)[/FONT]
    [FONT='Times New Roman','serif']2000= X/(1+0.15*6/12) + X/(1+0.15*12/12)[/FONT]
    [FONT='Times New Roman','serif']2000= 2.225x /1.23625[/FONT]
    [FONT='Times New Roman','serif']2.225X=2472.5[/FONT]
    [FONT='Times New Roman','serif']So, X=2472.5/2.225 = 1111.24[/FONT]
    [FONT='Times New Roman','serif'][/FONT]
    [FONT='Times New Roman','serif']if the datum date was changed to be 1/6/2001.calculate the value of each payment.[/FONT]
    [FONT='Times New Roman','serif']M= p(1+rt)[/FONT]
    [FONT='Times New Roman','serif']M= 2000 (1+0.15*1)= 2300[/FONT]
    [FONT='Times New Roman','serif']So, 2300 = X (1 + 0.15 * 6/12) + X[/FONT]
    [FONT='Times New Roman','serif']2300=2.075 X[/FONT]
    [FONT='Times New Roman','serif']X= 1108.43 [/FONT]
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  14. #14
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    If a person borrowed $2000 at 15%on the first of June 2000 to pay it in two equal times: the first on December 1st, 2000 & the other on June 1st,2001 & if the datum date was June 1st,2000. Calculate the value of each payment.
    X??

    p= m/(1+rt)
    2000= X/(1+0.15*6/12) + X/(1+0.15*12/12)
    2000= 2.225x /1.23625
    2.225X=2472.5
    So, X=2472.5/2.225 = 1111.24
    if the datum date was changed to be 1/6/2001.calculate the value of each payment
    M= p(1+rt)
    M= 2000 (1+0.15*1)= 2300
    So, 2300 = X (1 + 0.15 * 6/12) + X
    2300=2.075 X


    X= 1108.43

    Last edited by neverlosehope; June 16th 2007 at 03:24 PM. Reason: somthing wrong with my post
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  15. #15
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    I can't understand it plz explain thsi answer
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