Question

Interest rates determine the present value of future amounts. (Round to the nearest dollar.) (Click the icon to view Present Value of $1 table.) 6 (Click the icon to view Present Value of Ordinary Annuity of $1 table.) (Click the icon to view Future Value of $1 table.) 6 (Click the icon to view Future Value of Ordinary Annuity of $1 table.) Read the requirements. Requirement 1. Determine the present value of seven-year bonds payable with face value of $85,000 and stated interest rate of 10%, paid semiannually. The market rate of interest is 10% at issuance. (Round intermediary calculations and final answer to the nearest whole dollar.) Present Value When market rate of interest is 10% annually 0 Requirements 1. Determine the present value of seven-year bonds payable with face value of $85,000 and stated interest rate of 10%, paid semiannually. The market rate of interest is 10% at issuance. 2. Same bonds payable as in Requirement 1, but the market interest rate is 14%. 3. Same bonds payable as in Requirement 1, but the market interest rate is 8%. Print Done

Answer 1

Requirement (1):
The formula to compute present value of Price of bond (P) is as under:

Where,
C = Cash payments (interest) = 85000*10% = 8500
r = discount rate = 10% or 0.1
N = number of periods = 7 years semi annually = 7*2 = 14 periods
FV = Face value of bond = 85000

The formula can be simplified as:
P = (PV Annuity Factor r%, N years of C) + (PV factor r%, N years of FV)

PV Annuity Factor r%, N years = PVAF 10%, 14 years = 7.367
PV factor r%, N years = PVF 10%, 14 years = 0.263

+ P= ( +++

Therefore, P = (7.367 * 8500) + (0.263 * 85000)
P = 84974.5

Requirement (2):
r = 14%
Therefore,
PV Annuity Factor r%, N years = PVAF 14%, 14 years = 6.002
PV factor r%, N years = PVF 14%, 14 years = 0.160

Therefore, P = (6.006 * 8500) + (0.160 * 85000)
P = 64651

Requirement (3):
r = 8%
Therefore,
PV Annuity Factor r%, N years = PVAF 8%, 14 years = 8.244
PV factor r%, N years = PVF 8%, 14 years = 0.340

Therefore, P = (8.244 * 8500) + (0.340 * 85000)
P = 98974