S 2000 1 0 1 123 365 2067 40 1 d 2040 2067 40 1 d 123

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S = 2000 ° 1 + 0 : 1 ° 123 365 ±± : = $2067 : 40 2040 = 2067 : 40 ° 1 ° d ° 123 ° 30 365 ±± ) 2040 2067 : 40 = 1 ° d ° 123 ° 30 365 ± ) 93 365 d = 1 ° 2040 2067 : 40 ) d = 365 93 ° 1 ° 2040 2067 : 40 ± : = 0 : 0520 = 5 : 2% (b) Determine the net proceeds (or net pro°t) and rate of interest earned by the seller of the note. Pro°t: 2040 ° 2000 = $40 Yield rate: r = I Pt = 40 2000 ° 30 365 ± = 0 : 243 33 = 24 : 33% 2
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4. [8 marks ] A loan of $3164 will be repaid with 4 equal payments over a one year period. The °rst payment must be made immediately and the remaining payments in 4 months, 8 months and 12 months. If interest is charged at 8% per annum, determine the size of the equal payments taking your focal date to be (a) now and (b) 5 months from now. In each case draw a complete time diagram with all necessary labels. Be sure to label the focal date on your time diagrams. (a) Focal date: now; 3164 = X + X ° 1 + 0 : 08 ° 4 12 ±± ° 1 + X ° 1 + 0 : 08 ° 8 12 ±± ° 1 + X ° 1 + 0 : 08 ° 12 12 ±± ° 1 = X 1 + ° 1 + 0 : 08 ° 4 12 ±± ° 1 + ° 1 + 0 : 08 ° 8 12 ±± ° 1 + ° 1 + 0 : 08 ° 12 12 ±± ° 1 ! : = X (1 + 0 : 9740 + 0 : 9493 + 0 : 925 9) = 3 : 8492 X ) X = 3164 3 : 8492 : = 821 : 99 (b) Focal date: +5 months from now 3164 = X ° 1 + 0 : 08 ° 5 12 ±± + X ° 1 + 0 : 08 ° 1 12 ±± + X ° 1 + 0 : 08 ° 3 12 ±± ° 1 + X ° 1 + 0 : 08 ° 7 12 ±± ° 1 = X 1 + 0 : 08 ° 5 12 ± + 1 + 0 : 08 ° 1 12 ± + ° 1 + 0 : 08 ° 3 12 ±± ° 1 + ° 1 + 0 : 08 ° 7 12 ±± ° 1 !
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