Method and answers for attached
1. You would like to buy a machine. The conditions of the sale are as follows:
<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>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>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 = $419.16
<br>How much would you still owe after 5 years?
<br>At the end of 5 years, the future value of all the payments in 5 years is
<br>PMT = 59.88
<br>The Daily rate = 0.0219%
<br>Number of periods = 365*5=1825
<br>Then FV is calculated =$ 134,350.04
<br>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 ...