W5Tute 1001 - is the initial value of the loan To get V(1...

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Examples Jade decides to takes out a loan for \$100. She will repay the loan with a payment of \$30 in one year, a payment of \$40 in 2 years, and a lump sum of \$X in 3 years. The interest rates (nominal) for the period of the loan are: I Year 1: 4% compounded semi-annually; I Year 2: 5% compounded semi-annually; I Year 3: 6% compounded semi-annually. 1. Determine the eﬀective interest rate for each year. 2. Determine \$X. 3. Determine the value of the loan at time 0, 1, 2, 3 using: I forward recursion; I backward recursion. UNSW Week 5 ACTL1001 Tutorial

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Examples Determining interest rates and \$ X The corresponding eﬀective interest rates are: I Year 1: 1 . 02 2 - 1 = 0 . 0404 = 4 . 04% ; I Year 2: 1 . 025 2 - 1 = 0 . 050625 = 5 . 0625% ; I Year 3: 1 . 03 2 - 1 = 0 . 0609 = 6 . 09% . The present value of the loan repayments must be equal to the value of the loan, so we have: 100 = 30 1 . 0404 + 40 (1 . 0404)(1 . 050625) + X (1 . 0404)(1 . 050625)(1 . 0609) X = 100(1 . 0404)(1 . 050625)(1 . 0609) - 30(1 . 050625)(1 . 0609) - 40(1 . 0609) X = 40 . 08958095(8 decimal places) UNSW Week 5 ACTL1001 Tutorial
Examples Forward Recursion V (0) = 100

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Unformatted text preview: is the initial value of the loan To get V (1), accumulate the value of the loan forward with interest, and subtract the ﬁrst payment: V (1) = V (0)(1 + r (0))-C (1) = 100(1 . 0404)-30 = 74 . 04 To get V (2), apply interest, and subtract the second payment: V (2) = V (1)(1+ r (1))-C (2) = 74 . 04(1 . 050625)-40 = 37 . 788275 Repeat for V (3): V (3) = V (2)(1 + r (2))-C (3) = 37 . 788275(1 . 0609)-40 . 08958095 = 0 UNSW Week 5 ACTL1001 Tutorial Examples Backward Recursion V (3) = 0 is the value of the loan after it has been repaid For V (2), add the payment at time 3 and discount back to time 2: V (2) = V (3) + C (3) 1 + r (2) = 0 + 40 . 08958095 1 . 0609 = 37 . 788275 For V (1), add the payment at time 2 and discount back to time 1: V (1) = V (2) + C (2) 1 + r (1) = 37 . 788275 + 40 1 . 050625 = 74 . 04 Repeat for V (0): V (0) = V (1) + C (1) 1 + r (0) = 74 . 04 + 30 1 . 0404 = 100 UNSW Week 5 ACTL1001 Tutorial...
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This note was uploaded on 06/12/2011 for the course ASB 1001,2522, taught by Professor Nicole during the One '09 term at University of New South Wales.

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W5Tute 1001 - is the initial value of the loan To get V(1...

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