Question

hartford research issues bonds dated january 1 that pay interest semiannually on june 30 and december 31. the bonds have a $21,000 par value and an annual contract rate of 10%, and they mature in 10 years. (table b.1 (opens in a new tab), table b.2 (opens in a new tab), table b.3 (opens in a new tab), and table b.4 (opens in a new tab)) note: use appropriate factor(s) from the tables provided. round all table values to 4 decimal places, and use the rounded table values in calculations. complete this question by entering your answers in the tabs below. required 1a required 1b required 2a required 2b required 3a required 3b complete the below table to determine the bonds issue price on january 1 if the market rate at the date of issuance is 10%. note: round all table values to 4 decimal places. table values are based on: n = i = cash flow table value amount present value par (maturity) value interest (annuity) price of bonds

Explanation:

Step1: Set period & rate values

Since interest is semiannual:
$n = 10 \times 2 = 20$ periods
$i = \frac{10\%}{2} = 5\% = 0.05$

Step2: Find par value table value

For present value of $1$ (n=20, i=5%), table value = $0.3769$
Par amount = $\$21,000$
Present value of par: $21000 \times 0.3769 = \$7914.90$

Step3: Calculate semiannual interest

Semiannual interest amount: $\$21000 \times \frac{10\%}{2} = \$1050$

Step4: Find annuity table value

For present value of annuity of $1$ (n=20, i=5%), table value = $12.4622$
Present value of interest: $1050 \times 12.4622 = \$13085.31$

Step5: Sum present values for bond price

Bond price = Present value of par + Present value of interest

Answer:

Table values are based on:
$i =$	5%

Cash Flow	Table Value	Amount	Present Value
Interest (annuity)	12.4622	$\$1,050$	$\$13,085.31$
Price of bonds			$\$21,000.21$

(Note: The minor $0.21$ difference is due to table rounding; the bond price equals par value when market rate = contract rate, so this rounds to $\$21,000$)