Question

interest rates determine the present value of future amounts.

A Reference Periods 8 9 10 11 12 13 14 15 16 17 18 1% 2% 3% 0.990 0.980 0.971 0.9800.961 0.943 0.971 0.942 0.915 0.961 0.924 0.888 0.951 0.906 0.863 0.942 0.888 0.837 0.933 0.871 0.813 0.923 0.853 0.789 0.914 0.837 0.766 0.905 0.820 0.744 0.896 0.8040.722 0.887 0.788 0.701 0.879 0.773 0.681 0.870 0.758 0.661 0.861 0.743 0.642 0.853 0.728 0.623 0.844 0.714 0.605 0.836 0.700 0.587 0.962 0.925 0.889 0.855 0.822 0.790 0.760 0.731 0.703 0.676 0.650 0.625 0.601 0.577 0.555 0.534 0.513 0.494 Present Value of $1 7% 8% 9% 0.9520.943 0.935 0.926 0.917 0.907 0.890 0.873 0.857 0.842 0.864 0.840 0.816 0.7940.772 0.823 0.792 0.763 0.735 0.708 0.784 0.747 0.713 0.681 0.650 0.746 0.705 0.666 0.630 0.596 0.711 0.665 0.623 0.583 0.547 0.677 0.627 0.582 0.540 0.502 0.6450.592 0.544 0.500 0.460 0.614 0.558 0.508 0.463 0.422 0.585 0.527 0.475 0.429 0.388 0.557 0.497 0.444 0.397 0.356 0.530 0.469 0.415 0.368 0.326 0.505 0.442 0.388 0.340 0.299 0.481 0.417 0.362 0.315 0.275 0.458 0.394 0.3390.292 0.252 0.436 0.371 0.317 0.270 0.231 0.416 0.350 0.296 0.250 0.212 0.194 0. 377 0.3120.258 0.215 0.178 0.242 0.1990.164 10% 12% 0.909 0.893 0.826 0.797 0.751 0.712 0.683 0.636 0.621 0.567 0.564 0.507 0.513 0.452 0.467 0.404 0.424 0.361 0.386 0.322 0.350 0.287 0.319 0.257 0.290 0.229 0.263 0.205 0.239 0.183 0.218 0.163 0.1980.146 0.180 0.130 0.164 0.116 0.149 0.104 0.135 0.093 14% 0.877 0.769 0.675 0.592 0.519 0.456 0.400 0.351 0.308 0.270 0.237 0.208 0.182 0.160 0.140 0.123 0.108 0.095 0.083 0.073 0.064 15% 0.870 0.756 0.658 0.572 0.497 0.432 0.376 0.327 0.284 0.247 0.215 0.187 0.163 0.141 0.123 0.107 0.093 0.081 0.070 0.061 0.053 16% 0.862 0.743 0.641 0.552 0.476 0.410 0.354 0.305 0.263 0.227 0.195 0.168 0.145 0.125 0.108 0.093 0.080 0.069 0.060 0.051 0.044 1 20 21 0.820 0.811 0.673 0.554 0.456 0.660 0.538 0.439 TW SK OPS 22 > O

Answer 1

Present Value of Bond = Present Value of Bond's Interest payments + Present Value of bond's Maturity amount Semi Annual Payments of Interest = PMT Present Value of Ordinary Annuity = PVOA $ 7% Semi Annually Face Value of Bond = Interest rate Life of Bond Interest Payment (PMT)= 90,000.00 14% annually 7 years 6,300.00 $ Solution 1 Market Interest rate= 14% annually As the Bond pays semi annual interest, Rate would be 7% and life would be 14 PVOA @ 7% for 14 years (using table) = 8.745 Present Value of $1 @7% for 14 years = 0.388 Present Value of Bond's Interest Payments = PMT X PVOA $6300 x 8.745 $ 55,093.50 Bond Value x PV $90000 x 0.388 $ 34,920.00 Present Value of Bond's Maturity Amount = Present Value of Bond = $55094 +$34920 = $ 90,014

Solution 2 Market Interest rate= 16% annually As the Bond pays semi annual interest, Rate would be 8% and life would be 14 PVOA @ 8% for 14 years (using table) = 8.244 Present Value of $1 @8% for 14 years = 0.340 Present Value of Bond's Interest Payments = PMT x PVOA $6300 x 8.244 $ 51,937.20 Bond Value x PV $90000 x 0.388 $ 30,600.00 Present Value of Bond's Maturity Amount = Present Value of Bond = $51937 + $30600 = $ 82,537 Solution 3 Market Interest rate= 10% annually As the Bond pays semi annual interest, Rate would be 5% and life would be 14 PVOA @ 5% for 14 years (using table) = 9.899 Present Value of $1 @5% for 14 years = 0.505 Present Value of Bond's Interest Payments = PMT x PVOA $6300 x 9.899 $ 62,363.70 Bond Value x PV $90000 x 0.505 $ 45,450.00 Present Value of Bond's Maturity Amount = Present Value of Bond = $62364 + $45450 = $ 1,07,814

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