Chapter 3Mathematics of FinanceMathematics of FinanceSection 1Simple Interestp3.1 Simple Interest Definition:Definition:I = PrtwhereI = interest earned P = principal (amount invested) r= interest rate (as a decimal) 2()t = time An ExampleFind the interest on a boat loan ofFind the interest on a boat loan of $5,000 at 16% for 8 months. 3ExampleFind the interest on a boat loan ofFind the interest on a boat loan of $5,000 at 16% for 8 months. Solution: Use I = Prt• I = 5,000(0.16)(0.6667)• (8 months = 8/12 of one year 40.6667 years)• I = $533.33Total Amount to Be Paid BackThe total amount to be paid back for the boat loan wouldThe total amount to be paid back for the boat loan would be $5000 plus the interest of $533.33, for a total of $5,533.33.5Present Value and Future ValueA=P+PrtA = P + Prt= P (1 + rt)whereA = amount, or future valueP = principal, or present value6r = annual simple interest rate (as a decimal)t = time in yearsAnother ExampleFind the total amount due on a loan of $600 at 16% interestFind the total amount due on a loan of $600 at 16% interest at the end of 15 months.7Another ExampleFind the total amount due on a loan of $600 at 16% interestFind the total amount due on a loan of $600 at 16% interest at the end of 15 months. Solution: A = P (1 + rt) A = 600(1+0.16(1.25)) A = $720.00 8Interest Rate Earned on a NoteWhat is the annual interest rate earned by a 33-day T-bill with a maturity value of $1,000 that sells for $996.16? 9Interest Rate Earned on a NoteSolutionSolution:Use the equationA=P(1 +rt)WllSolution:Use the equation A= P (1 + rt)1,000 = 996.16331360r⎛⎞⎛⎞+⎜⎟⎜⎟⎝⎠⎝⎠1000 = 996.16(1+r(0.09166))1000=996.16+996.16(0.09166)r1000 996 16→→We normally use 360 days for a financial year101000-996.16996.16(0.09166)0.042 4.2%rr=→==Another ApplicationA department storeA department store charges 18.6% interest (annual) for overdue accounts. How much interest will be owed on a $1080 account that is 3 months overdue?11Another ApplicationsolutionA department storeSolution:A department store charges 18.6% interest (annual) for overdue accounts. How much interest will be owed on a $1080 account that is 3 months overdue?Solution: I = PrtI = 1080(0.186)(0.25)I=$50.2212I
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