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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 rst 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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