HW2Solutions - ACF329 Interest Theory Fall 2010 University...

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Unformatted text preview: ACF329 Interest Theory Fall 2010 University of Texas at Austin HW 2 - Solutions Instructor: Milica Cudina 3.2.2. Let i denote the annual effective interest rate, and let v = 1 1+ i . The present value of Tracys annuity-immediate can be expressed as 493 = Xa n i = X 1- v n i = X i (1- v n ) . The present value of Garys annuity-immediate is 2748 = 3 Xa 2 n i = 3 X 1- v 2 n i = X i [3(1- v 2 n )] . So, X i = 493 1- v n = 2748 3(1- v 2 n ) . Hence, 493 1- v n = 916 1- v 2 n and so 493(1- v 2 n ) = 916(1- v n ) . Thus, 493(1- v n )(1 + v n ) = 916(1- v n ) . Finally, 1 + v n = 916 493 v n = 423 493 . 858 . 3.2.4. The loan repayment scheme is an annuity with 360 payments, the effective interest rate j = 0 . 0585 / 12 = 0 . 004875 per period and every payment equal to 820- 240. Using your calculator, you set N = 360 , I/Y = 0 . 4875 and PMT = 580. Then you compute (CPT) the present value (PV) and get $98, 314.93. Finally, you can add the down-payment of $13,200 to get the total maximum price of $111,514.93.$13,200 to get the total maximum price of $111,514....
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HW2Solutions - ACF329 Interest Theory Fall 2010 University...

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