Solutions to Extra Problems 2

Solutions to Extra Problems 2 - ACTSC 231 Solutions to...

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Unformatted text preview: ACTSC 231 Solutions to Extra Problem set 2 ¡ ¡ ¥ 360 1. a. 100000 1 d 170 96000 d 1 360 170 m i 100000 96006 365 m b. m (eff. rate per 170 days) i 96006 170 365 year compounded every 170 days or 170 times per year. 2.The value at time three 100e 1 200e 2 500e 5 100e 1 200e 2 500e .01t | 3 2 5 100e ln 1.03 1.01 200e ln 1.03 1.02 100 1. 03 1. 01 1314. 17 200 1. 03 1. 02 3. 1 i 4 3 i4 4 3 40 1 4. .1 1.25 15e .1 6.5 10e .1 1.25 15e .1 6.5 2500e .1t 1000e .1 1.25 1500e .1 6.5 e .1t . 1t ln 10e 25 25 .1 1.25 15e .1 6.5 t 10 ln 10e 4. 06 years 25 5. Principal (amt borrowed PV of payments): 24 25 3000 1 .10 4000 1 .08 4732. 77 2 2 2 PV of payments (consolidated loan): X X 1 .12 1. 889 996 4X 2 4732.77 1. 889 996 4X 4732. 77 X 2504. 12 1.889 996 4 1 6. 7% for 6 months: 1. 07 2 1. 034 408 1 1. 021 778 2 option A gives more interest 9% for 3 months: 1. 09 4 7% for 18 months: 1. 07 1.5 1. 106816 6 9% for 15 months: 1. 09 1.25 1. 113 738 2 option B gives more interest 7. Let X be the monthly payment. The PV of the payments 1 month before the first payment is Xa 48|.5% and the PV 13 months before the first payment is X 1. 005 12 a 48|.5% 20000 20000 X 1. 005 12 a 48|.5% X 498. 67 12 1 1.005 48 i 8. payments of $300 every six months for 4 years 300a 8|j 1 , where j 1 , but we are given 2 4 i 10% 2 4 2 4 2 i2 1 i2 1 i4 j1 1 .10 1 5. 0625% 2 4 i4 $100 every 3 months for 6 years 100a 24|j 2 , where j 2 . 025 This starts at the end of 4 4 years, so bringing that back to time zero gives us: 1. 025 4 4 100a 24|2.5% The overall PV is: 300a 8|5.0625% 1. 025 16 100a 24|2.5% 3138. 85 9. The value 6 months before the first payment is 600 , where j i2 j 1. 08 1/2 1 3. 9230485% 2 Move this value forward 5 months (so that it is 1 month before the first payment) 600 1. 08 5/12 .039230485 15, 792. 62 ¡ ¤£ ¡ ¥ ¡ ¤£ ¡  ¡ © ¡ ©   1.005 .005 2 ¤£ ¤ £  ¡ ¢ ¤£ ¥ ¡¥  ¤ £  ¡  © ¡ ¢ ¡ ¢ ¥ ¡ ¤£ © ¡§ ¥ ¦ ¢§ ¦ ¥ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¢ ¢ ¡ © ©§¦ ¥ ¡ ¡ ¤ £  ¤ £  ©§ ¦ ¥  ¢    ¤£ ¢ 4 4 10 1 © © 100 © 100 100 500e ln 100 1.03 1.05 100 500 1. 03 1. 05 100 § 100e 100 ln 1 .01t | 3 1 200e 100 ln 1 500e 100 ln 1 ¦  ©§ © ¦  © ©§ © ¦  ¡ ¡ ¡ ¡ ¡ ¡§¦ © ¡  ¡   ¥ © ¡§ ¦  ¡  ¡ © Þ t dt Þ t dt Þ ¨ ¨ § ¦ ¥  ¤£ ¨ 3 3 3 t dt Þ 3 1 1 .01t dt ¡§¦ ¡ ¢ 96000 8. 47% 100000 100000 96006 8. 93% 96006 ¡ ¥ ¤£ ¡ ¤£ ¡ ¡ ©  © nominal rate per Þ 3 1 1 .01t dt Þ 3 1 1 .01t dt .01t | 3 5 ¡ ¤£ ¡ © ¥ ¡§¦   ¡ ¢ ...
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This note was uploaded on 04/07/2010 for the course ACTSC 231 taught by Professor Chisholm during the Winter '09 term at Waterloo.

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