A gilt with a face value of £100 and 2 years to maturity pays a 6% annual coupon. It is quoted at a price of £99.09. What is its yield to maturity (YTM)? Present Value Table Present value of 1 i.e. (1 + r)–n Where r = discount rate n = number of periods until payment Periods Discount rate (r) Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%1 0.990 0.980 0.971 0.962 0.952 0.942 0.933 0.923 0.914 0.9052 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.8263 0.971 0.942 0.914 0.887 0.861 0.837 0.813 0.790 0.768 0.7464 0.961 0.924 0.888 0.853 0.819 0.786 0.754 0.723 0.693 0.6655 0.951 0.888 0.837 0.789 0.747 0.708 0.672 0.636 0.603 0.5736 0.942 0.853 0.789 0.735 0.681 0.630 0.582 0.537 0.495 0.4567 0.933 0.837 0.758 0.698 0.636 0.577 0.524 0.476 0.433 0.3948 0.923 0.820 0.733 0.652 0.579 0.513 0.454 0.401 0.354 0.3139 0.914 0.804 0.711 0.627 0.549 0.481 0.422 0.371 0.325 0.28510 0.905 0.788 0.693 0.606 0.528 0.461 0.404 0.355 0.313 0.27811 0.896 0.772 0.676 0.577 0.487 0.417 0.356 0.303 0.257 0.21712 0.887 0.757 0.661 0.563 0.474 0.397 0.331 0.274 0.226 0.18613 0.879 0.741 0.646 0.547 0.457 0.380 0.315 0.260 0.215 0.17814 0.870 0.726 0.632 0.532 0.442 0.366 0.303 0.250 0.207 0.17115 0.861 0.711 0.618 0.518 0.429 0.353 0.291 0.240 0.198 0.163 Annuity Table Present value of an annuity of 〖(1-(1+r)〗^(-n))/r Where r = discount raten = number of periods Periods Discount rate (r) Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%1 0.990 0.980 0.971 0.962 0.952 0.942 0.933 0.923 0.914 0.9052 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.7373 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.4874 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.1705 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.7916 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.3557 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.8688 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.3359 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.75910 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.14511 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.49512 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.81413 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 7.10314 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.786 7.36715 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559 8.061 7.606
A gilt with a face value of £100 and 2 years to maturity pays a 6% annual coupon. It is quoted at a price of £99.09. What is its yield to maturity (YTM)?
Present value of 1 i.e. (1 + r)–n Where r = discount rate
n = number of periods until payment
Periods
Discount rate (r)
Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 0.990 0.980 0.971 0.962 0.952 0.942 0.933 0.923 0.914 0.905
2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826
3 0.971 0.942 0.914 0.887 0.861 0.837 0.813 0.790 0.768 0.746
4 0.961 0.924 0.888 0.853 0.819 0.786 0.754 0.723 0.693 0.665
5 0.951 0.888 0.837 0.789 0.747 0.708 0.672 0.636 0.603 0.573
6 0.942 0.853 0.789 0.735 0.681 0.630 0.582 0.537 0.495 0.456
7 0.933 0.837 0.758 0.698 0.636 0.577 0.524 0.476 0.433 0.394
8 0.923 0.820 0.733 0.652 0.579 0.513 0.454 0.401 0.354 0.313
9 0.914 0.804 0.711 0.627 0.549 0.481 0.422 0.371 0.325 0.285
10 0.905 0.788 0.693 0.606 0.528 0.461 0.404 0.355 0.313 0.278
11 0.896 0.772 0.676 0.577 0.487 0.417 0.356 0.303 0.257 0.217
12 0.887 0.757 0.661 0.563 0.474 0.397 0.331 0.274 0.226 0.186
13 0.879 0.741 0.646 0.547 0.457 0.380 0.315 0.260 0.215 0.178
14 0.870 0.726 0.632 0.532 0.442 0.366 0.303 0.250 0.207 0.171
15 0.861 0.711 0.618 0.518 0.429 0.353 0.291 0.240 0.198 0.163
Present value of an annuity of
〖(1-(1+r)〗^(-n))/r
Where r = discount rate
n = number of periods
Periods
Discount rate (r)
Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 0.990 0.980 0.971 0.962 0.952 0.942 0.933 0.923 0.914 0.905
2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.737
3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487
4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170
5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791
6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355
7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868
8 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335
9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759
10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145
11 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495
12 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814
13 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 7.103
14 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.786 7.367
15 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559 8.061 7.606
Step by step
Solved in 2 steps
