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    Present Value of Annuity Streams

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    How would you calculate the present and future value of the following annuity streams?

    a. $5,000 received each year for 5 years on the last day of each year if your investments pay 6 percent compounded annually.

    b. $5,000 received each quarter for 5 years on the last day of each quarter if your investments pay 6 percent compounded quarterly.

    c. $5,000 received each year for 5 years on the first day of each year if your investments pay 6 percent compounded annually.

    d. $5,000 received each quarter for 5 years on the first day of each quarter if your investments pay 6 percent compounded quarterly.

    © BrainMass Inc. brainmass.com December 24, 2021, 10:28 pm ad1c9bdddf
    https://brainmass.com/business/the-time-value-of-money/present-value-annuity-streams-479789

    SOLUTION This solution is FREE courtesy of BrainMass!

    Thank you for asking BrainMass. Here you go:

    a. $5,000 received each year for 5 years on the last day of each year if your investments pay 6 percent compounded annually.
    Cash Flow Stream: Annuity
    Type of annuity: Arrears
    Annual cash flow C= $5,000
    Number of years t = 5 years
    Frequency of compounding in a year f= 1
    Annual Interest rate R= 6%
    Interest rate for compouding period r = R/f=6%/1=6%
    PV of an annuity in arrears=C/r*(1-1/(1+r)^(f*t))= 5000/6%*(1-1/(1+6%)^(1*5))=$21061.82

    b. $5,000 received each quarter for 5 years on the last day of each quarter if your investments pay 6 percent compounded quarterly.
    Cash Flow Stream: Annuity
    Type of annuity: Arrears
    Quarterly cash flow C= $5,000
    Number of years t = 5 years
    Frequency of compounding in a year f= 4
    Annual Interest rate R= 6%
    Interest rate for compouding period r = R/f=6%/4=1.5%
    PV of an annuity in arrears=C/r*(1-1/(1+r)^(f*t))= 5000/1.5%*(1-1/(1+1.5%)^(4*5))=$85843.19

    c. $5,000 received each year for 5 years on the first day of each year if your investments pay 6 percent compounded annually.
    Cash Flow Stream: Annuity
    Type of annuity: Advance
    Annual cash flow C= $5,000
    Number of years t = 5 years
    Frequency of compounding in a year f= 1
    Annual Interest rate R= 6%
    Interest rate for compouding period r = R/f=6%/1=6%
    PV of an annuity in advance =PVof annuity in arrears * (1+r) = $21061.82*(1+6%)=$22325.53

    d. $5,000 received each quarter for 5 years on the first day of each quarter if your investments pay 6 percent compounded quarterly.
    Cash Flow Stream: Annuity
    Type of annuity: Advance
    Quarterly cash flow C= $5,000
    Number of years t = 5 years
    Frequency of compounding in a year f= 4
    Annual Interest rate R= 6%
    Interest rate for compouding period r = R/f=6%/4=1.5%
    PV of an annuity in advance =PVof annuity in arrears * (1+r) = $85843.19*(1+1.5%)=$87130.84
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    FUTURE VALUE
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    Check the attached sheet. The calculation are complex to do manual thats why excel is used.

    You can also use Future Value of Annuity tables to computes Future value

    Future Value Annuity Factor for 5 payments for 6% = 5.637
    So,

    (a) Future Value = 5000*5.637 = $28,185

    Future Value Annuity Factor for 20 (5*4) quarterly payments for 1.5% per quarter = 23.124

    (b) Future Value = 5000*23.124 = $115,620

    Similiary for (c) Future Value = 5000*5.975 = $29,875
    (d) Future value = 5000*23.471 = $117,355

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 10:28 pm ad1c9bdddf>
    https://brainmass.com/business/the-time-value-of-money/present-value-annuity-streams-479789

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