Problem Set 6:ACTSC 231 Mathematics of Finance, Fall 2010Q1.Carefully describe what each of the following symbols measures and calculate theirvalues to the nearest 0.0001:(a) 200a(4)10 6%;(b) 1200¨s(12)20 4%.Q2.Compare these four symbols ¨an i, ¨a(m)n i, a(m)n iand an iby calculating their values atn= 48,m= 12 andi= 5%.Q3.A loan of 20,000 is to be repaid in 20 years using the sinking fund method. You aretold that the sinking fund payment made at the end of each year is 744.31, and thatthe annual effective interest rateisuch that the amortization method based onihasan annual payment equal to the total annual payment in the sinking fund method is8.7%. Determine the annual effective interest rateicharged on the loan.Q4.For a loan of $1,000, level interest payments are made at the end of each year for 10years with an annual effective interest rate of 5%, and the principal amount is repaid atthe end of 10 years. At the end of each year, the borrower makes level annual paymentto a sinking fund that earns interest at an annual effective rate of 4%. At the end of
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