Final answer:
To calculate the current value of the bond, you need to calculate the present value of each annual coupon payment and the present value of the bond's principal at maturity. Use the formula PV = CF / (1+r)^n to calculate the present value of each cash flow.
Step-by-step explanation:
To calculate the current value of the bond, we need to calculate the present value of each annual coupon payment and the present value of the bond's principal at maturity. The formula to calculate the present value of a future cash flow is:
PV = CF / (1+r)^n
Where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of periods in the future.
Using this formula, the present value of each annual coupon payment would be:
Present value of coupon = Coupon payment / (1 + r)^n
Since the coupon rate is 5% and the bond pays annually, the coupon payment would be $2,500 ($50,000 * 5%). Considering a discount rate of 0.3%, the present value of the coupon payments would be:
Present value of coupon = $2,500 / (1 + 0.003)^1 + $2,500 / (1 + 0.003)^2 + $2,500 / (1 + 0.003)^3 + $2,500 / (1 + 0.003)^4 + $2,500 / (1 + 0.003)^5
Calculating this expression will give you the present value of the coupon payments. Finally, we need to calculate the present value of the principal at maturity.
Present value of principal = Principal / (1 + r)^n
Using the same discount rate, the present value of the principal would be:
Present value of principal = $50,000 / (1 + 0.003)^5
Calculating this expression will give you the present value of the principal. Adding the present value of the coupon payments and the present value of the principal will give you the current value of the bond.