# Calculation of repayments, value of shares and bonds

Method and answers for attached

© BrainMass Inc. brainmass.com June 3, 2020, 5:18 pm ad1c9bdddfhttps://brainmass.com/business/bond-valuation/calculation-of-repayments-value-of-shares-and-bonds-20736

#### Solution Preview

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 ...