10 00 46 DECODE VCE FURTHER MATHEMATICS Instructions Answer all questions by circling one of the bolded letters in the given list of responses. Choose the response that is correct for the question. A correct answer scores 1; an incorrect answer scores 0. Marks will not be deducted for incorrect answers. No marks will be given if more than one answer is completed for any question. Unless otherwise indicated, the diagrams in this book are not drawn to scale. Question 1 Consider the recurrence relation below. Co = 3.3, Cn+1 = 3.3Cn+ 3 The value of C4 is closest to A. 48.83 B. 48.84 C. 164.16 D. 544.73 E. 544.74 Question 2 If the sequence Sn satisfies the recurrence relation Sn+1 = 25, + 1, then S3 is equal to A. 250 + 7 B. 450 + 2 C. 850 + 7 D. 450 + 3 E. 850 +5 Question 3 Suppose that Vn is the value of a perpetuity after n payments, and that Vn satisfies the recurrence relation Vn+1 = 1.008Vn - 400. The value of Vo is A. 40 000 B. 50 000 400 = C. 60 000 D. 70 000 E. 80 000 DO Volume 3 Solutions Manual DiARE Scan QR codeTM to open!47 DECODE VCE FURTHER MATHEMATICS Question 4 A tow trailer depreciates by $150 every year and has a scrap value of $800. It takes 15 years for the trailer to reach its scrap value. The initial value of the trailer is A. $2050 B. $2250 C. $3050 D. $3250 E. $3750 Question 5 The first three lines of an amortisation table for a loan are shown below. Some information is missing. Annual payments of $45 000 are made towards repaying the loan, and the loan gains interest at a rate of 3.3% per annum. Payment Payment Interest Principal Balance of number reduction loan 0 0.00 0.00 0.00 500 000.00 1 45 000.00 16 500.00 28 500.00 471 500.00 2 45 000.00 15 559.50 The reduction in the principal of the loan after payment 2 is A. $15 559.50 B. $28 500.00 C. $29 440.50 D. $443 000.00 E. $471 500.00 Question 6 Morty takes out a mortgage (home loan) of $550 000. He repays the mortgage in 25 years with yearly repay- ments of $35 000. Interest on the mortage is calculated immediately before each payment is made. The annual rate at which the mortgage gains interest is closest to A. 3.9% B. 4.0% 4.1% D. 4.2% E. 4.3% Volume 3 0180 Solutions Manual Scan QR code TM to open! ORDECODE VCE FURTHER MATHEMATICS 48 Question 7 Lezly has won $100 000 000 at the pokies. He decides to invest this money in an annuity in order to provide a better life for his child. The annuity will earn interest at a rate of 3.7% per annum compounding fortnightly, and will last for exactly 55 years. The annuity will pay $N fortnighty. The value of N is closest to A. 163 736 N= 55 x 26 B. 193 532 1: 3.7 C. 444 853 PV : - 1000000 00 D. 1891 557 PMT =9 16375- 73 E. 2248 387 FV = O Question 8 Ply - 26 The sequence Sn can be defined by the formula Sn = ant + b for all n 2 0, where a and b are constants. Which of the following is not a possible recurrence relation that Sn could satisfy? A. Sn+1 = 25n B. Sn+1 = Sn C. Sn+1 = 0Sn D. Sn+1 = Sn XSn E. Sn+1 = Sn + 1 END OF TEST Download the solutions manual at www.decodeguides.com.au or scan the QR code below! Volume 3 Solutions Manual