Tutorial 6 solution

# Tutorial 6 solution - 07/08 Semester II THE UNIVERSITY OF...

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07/08 Semester II THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1802 Financial Mathematics Solutions to Tutorial 6 Mar 14, 2008 1. The semi-annual payments on the loan are 50 plus 2% of the unpaid balance. Thus the AV of the reinvested installments at the end of the 10 years is AV = 50 s 20 | 0 . 025 + ( Ds ) 20 | 0 . 025 = 50 s 20 | 0 . 025 + 1 . 025 20 ( Da ) 20 | 0 . 025 = 50 s 20 | 0 . 025 + 1 . 025 20 20 - a 20 | 0 . 025 0 . 025 = \$1566 . 340 Let the annual eﬀective yield rate on the loan be i . Then 1 , 000(1 + i ) 10 = 1566 . 340 i = 0 . 04589623 = 4 . 6% . 2. The loan balance immediately after the 12th payment is: 23 , 115(1 . 03) 12 - 1 , 000 s 12 | 0 . 03 = 18 , 764 . 43 . This loan balance is reﬁnanced at 3 . 5% per quarter, so the balance after another 12 payments is 18 , 764 . 43(1 . 035) 12 - 1 , 000 s 12 | 0 . 035 = 13 , 752 . Some students don’t understand why the prospective method is not appropriate for this question. The present value of the loan is constant. The payments will change if the interest

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Tutorial 6 solution - 07/08 Semester II THE UNIVERSITY OF...

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