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    Calculation of repayments, value of shares and bonds

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    1. You would like to buy a machine. The conditions of the sale are as follows:
    <br>
    <br>Price without discount: $100,000;
    <br>Final bullet payment: $30,000
    <br>Repayment period: 7 years, compounded daily and payable weekly
    <br>APR equals 8 percent.
    <br>A choice must be made for borrowing the initial deposit of 15,000. Is it more appropriate to borrow at the 6 percent p.a. payable as a lump sum after two years, or repay the debt in four equal semiannual installments of $4035.40. In the latter case the interest rate is 6 percent compounded semiannually.
    <br>
    <br>
    <br>What is the Effective Annual Rate?
    <br>In the first case, the EAR = 6%
    <br>In the second case, the semiannual rate is R=6/2 = 3%
    <br>Then the effective annual rate is:
    <br>EAR = ((1 + R)^ 2) - 1 = 6.1%
    <br>Obviously, the EAR in the second case is higher than that of the first case.
    <br>
    <br>Calculate the weekly payment?
    <br>The Daily rate is 8%/365 = 0.0219%
    <br>The Present Value is $100,000
    <br>Final Value is $30,000
    <br>Number of periods = 365*7=2555
    <br>Then calculate payment each day is: PMT = $59.88
    <br>(refer to the attach EXCEL file for calculation)
    <br>So the weekly payment = 7*PMT = 7*$59.88 = $419.16
    <br>
    <br>How much would you still owe after 5 years?
    <br>At the end of 5 years, the future value of all the payments in 5 years is
    <br>PMT = 59.88
    <br>The Daily rate = 0.0219%
    <br>Number of periods = 365*5=1825
    <br>Then FV is calculated =$ 134,350.04
    <br>
    <br>However, the FV of the Price without discount: $100,000 is =-FV(r, 365*5, 0, PV) = $149,175.93
    <br>Moreover, the present value at of Final bullet payment at the end of 5 years ...

    $2.49

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