Answer:
The present value of this 10 year bond will be it's face value i.e $83,000
Step-by-step explanation:
Assumption: Since the question does not specify whether coupon rate and market interest rates provided are on per annum basis, it has been assumed both rates are on per annum basis i.e 10% per annum and the question has been solved accordingly.
Now, present value of a bond is it's future stream of interest payments and principal repayment upon maturity, both discounted at yield to maturity (ytm) i.e market rate of interest i.e 10%.
Since in this case, both coupon rate of interest and yield to maturity are the same i.e 10%. this is a FACE VALUE BOND and thus, it's present value will be equal to it's face value i.e $83,000.
PV = $4150 × 12.462210 (cumulative present value discounting factor at 5% for 20 periods) + $83000 × 0.37688 (present value discounting factor at 5% for 20th period)
PV= $51718.1715 + $31,2814.8270
PV = $83,000 (approx.)