Question

A professional company is doing the job and will be paid over a 4-year period with year-end payments of $6,861.64. The market interest rate is 10%. How much will I be paying for the fencing job in today's dollars? a) $17,075.03 b) $23,926.22 c) $36,602.50 d) None of the above Today you plan to deposit a lumpsum amount in a bank account that will earn an annual interest rate of 5%. The purpose of this deposit is to earn $2,000 interest income every year to donate to charity at each year-end forever. What lumpsum amount must you deposit today? a) $40,000 b) $50,000 c) $80,000 d) $140,000 e) None of the above A 5-year $50,000 loan is to be paid off by monthly payments of $1,410.20 at each month-end. What monthly interest rate and effective annual interest rate are being charged on the loan? a) 0.5%;6.17% b) 1%;12.68% c) 1.5%;19.56% d) 2%;26.82% e) None of the above A bank's certificate of deposit carrying 12% annual interest rate will pay $1,000 at the end of one year from today. Will the certificate sell at a higher price if the interest is compounded semi-annually rather than annually? True False

Answer 1

When the market interest rate rises to 9% over the initial 6% for the 10-year bond, you would expect to pay less than the face value of the bond. To calculate the maximum price, you discount the bond's expected payment of $10,600 at the 9% interest rate, which yields a maximum price you'd be willing to pay of $9,724.77.

Step-by-step explanation:

Calculating the Price of a Bond with a Lower Market Interest Rate

If the local water company has issued a $10,000 ten-year bond at a 6% interest rate, and you are considering purchasing it one year before maturity when the market interest rates are at 9%, you would expect to pay less than the face value of the bond. This is because the bond's fixed interest payments are less attractive when newly available bonds are offering a higher interest rate.

To calculate the price you would be willing to pay for this bond, you need to discount the bond's remaining cash flow, which is the final interest payment plus the $10,000 principal, back at the current market interest rate of 9%. The expected payments from the bond one year from now are $10,600 ($600 in interest plus the $10,000 principal). Using the formula for the present value of a single sum, the calculation would be:

Price = Expected Payment / (1 + Market Interest Rate)
Price = $10,600 / (1 + 0.09)
Price = $10,600 / 1.09
Price = $9,724.77

You therefore would not want to pay more than $9,724.77 for the bond.