Question

Determine the present value of five- year bonds payable with face value of $88000 and stated interest rate of 14%, paid semiannually. The market rate of interest is 14% at issuance.
When market rate iof interest is 14% annually______(present value)

Answer 1

present value of bond = [present value of annuity factor * interest payment] + [present value factor * face value]

here,

present value of annuity factor = [1-(1+r)^(-n)] / r

here,

r = 14% per annum =>14%*6/12=>7% =>0.07.

n = 5 years * 2 semi annual periods =>10 periods.

[1-(1.07)^(-10)]/0.07

=>0.4916507/0.07

=>7.02358143.

interest payment = $88,000*14%*6/12 =>$6,160.

present value factor = 1/(1+r)^n

=>1 / (1.07)^10

=>0.50834929.

face value = $88,000.

now,

present value of bond = [7.02358143*$6160] + [0.50834929*88000]

=>$88,000.