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    Calculating present and future values

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    13. The future value of $200 received today and deposited for three years in an account which pays semiannual interest of 8 percent is ______.
    A. $253.00
    B. $252.00
    C. $158.00
    D. $134.66

    14. The future value of $100 received today and deposited at 6 percent for four years is
    A. $126.
    B. $ 79.
    C. $124.
    D. $116.

    15-19. Calculate the present value of the annuity assuming that it is an ordinary annuity.

    Case Amount of Annuity Interest Rate Period / Years
    A $14,000 9% 3
    B $17,500 13% 15
    C $975 18% 7
    D $1,127,000 4% 9
    E $10,000 7% 3

    20-24. For each of the cases shown below in the table, calculate the present value of the cash flow:

    Case Single Cash Flow Interest Rate End of Periods / Years
    A $13,000 10% 5
    B $34,000 17% 25
    C $16,000 6% 18
    D $210,000 15% 15
    E $90,000 20% 9

    25-29 For each of the cases shown below in the table, calculate the future value of the cash flow:

    Case Single Cash Flow Interest Rate End of Periods / Years
    A $3,000 10% 7
    B $44,000 12% 5
    C $6,000 8% 10
    D $27,000 16% 12
    E $99,000 20% 6

    Calculate the above future values in questions 25-29 as semi annual and quarterly compounding.

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    https://brainmass.com/business/annuity/calculating-present-and-future-values-374896

    Solution Preview

    Please refer attached file for better clarity of formulas.

    13.
    Present Value of deposit=PV=$200
    Semi annual interest rate=i=8%/2=4%
    Number of periods=n=3 years=6 (semi annual periods)
    Future Value of deposit=PV*(1+i)^n=200*(1+4%)^6=253.06

    Answer is A. $253

    14.

    Present Value of deposit=PV=$100
    Annual interest rate=i=6%
    Number of periods=n=4 years
    Future Value of deposit=PV*(1+i)^n=100*(1+6%)^4=126.2477

    Answer is A. $126

    15-19.

    Case A:
    Amount of annuity=R=$14000
    Interest rate=i=9%
    Periods=n=3 years
    Present Value of annuity=PV=R*(1-1/(1+i)^n)/i=14000*(1-1/(1+9%)^3)/9%=$35,438.13

    Case B:
    Amount of annuity=R=$17500
    Interest rate=i=13%
    Periods=n=15 years
    Present Value of annuity=PV=R*(1-1/(1+i)^n)/i=17500*(1-1/(1+13%)^15)/13%=$113,091.63

    Case C:
    Amount of annuity=R=$975
    Interest rate=i=18%
    Periods=n=7 years
    Present Value of annuity=PV=R*(1-1/(1+i)^n)/i=975*(1-1/(1+18%)^7)/18%=$3,716.24

    Case D:
    Amount of annuity=R=$1,127,000
    Interest rate=i=4%
    Periods=n=9 years
    Present Value of annuity=PV=R*(1-1/(1+i)^n)/i=1127000*(1-1/(1+4%)^9)/4%=$8,379,618.7

    Case ...

    Solution Summary

    There are basic 17 problems related to time value of money concepts. Solutions depict the methodology to calculate Present and future values in different cases.

    $2.19

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