Question
Determine the present value of an amortizable coupon bond with a face value of $50,000, which makes annual payments of $15,000 and whose annual issuance rate is 7%, with a maturity date of 4 years and an IRR rate of 8%.
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Answer to a math question Determine the present value of an amortizable coupon bond with a face value of $50,000, which makes annual payments of $15,000 and whose annual issuance rate is 7%, with a maturity date of 4 years and an IRR rate of 8%.
Gerhard
4.592 Answers
1. Calculate the present value of each coupon payment:
PV_1 = \frac{15000}{(1+0.08)^1} = \frac{15000}{1.08} = 13,888.88
PV_2 = \frac{15000}{(1+0.08)^2} = \frac{15000}{1.1664} = 12,857.14
PV_3 = \frac{15000}{(1+0.08)^3} = \frac{15000}{1.2597} = 11,904.76
PV_4 = \frac{15000}{(1+0.08)^4} = \frac{15000}{1.3605} = 11,029.41
2. Calculate the present value of the face value:
PV_{FV} = \frac{50000}{(1+0.08)^4} = \frac{50000}{1.3605} = 36,764.71
3. Sum the present values to get the bond's present value:
PV = 13,888.88 + 12,857.14 + 11,904.76 + 11,029.41 + 36,764.71 = 86,444.90
2. Calculate the present value of the face value:
3. Sum the present values to get the bond's present value:
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