 Knowing how to reduce your debt is important, but you need to understand how to change some of the variables of an annuity to do it. Loan Amount$19,000 Annual Interest Rate 6.5 %8%6.5% Term3 years 6 years Payment Frequency Monthly Amount Owed at end of Term $23,078.76$24,134.50$28, Monthly Payments $641.08$670.40$389.35

 Susan is considering two investment options for saving $500 a month. Option 1: Monthly payment of $500, invested at 6% per year, compounded monthly. Option 2: Semi-monthly payment (on the 15 th and the 30 th of each month) of $250, invested at 5.85% per year, compounded semi-monthly.

PaymentFrequencyInterestInterest Frequency OPTION A$500Monthly6%/yearCompounded monthly OPTION B$250Semi-monthly5.85%/yrComp. semi-monthly After 1 year, the Future Value of each investment will be FV = PV(1 + i) n OPTION A: PV: 500, i = 0.06/12 = 0.005, n = 12 FV1 = 500(1.005) 12 The 1 st payment gets interest over 12 months. FV2 = 500(1.005) 11 The 2 nd payment gets interest over 11 months. FV3 = 500(1.005) 10 The 3 rd payment gets interest over 10 months, etc. [FV1 = $503] + [FV2 = $502.75] + [FV3 = $502.50] + [FV4] + … + [FV12] OPTION B: PV: 250, i = /24 = , n = 24 FV1 = 250( ) 24 1 st payment gets interest over 24 semi-months. FV2 = 250( ) 23 2 nd payment gets interest over 23 semi-months. FV3 = 250( ) 22 3 rd payment gets interest over 22 semi-months, etc. [FV1 = $265.04] + [FV2 = $264.40] + [FV3 = $263.76] + [FV4] + … + [FV24]

 OPTION A: [FV1 = $503] + [FV2 = $502.75] + [FV3 = $502.50] + [FV4] + … + [FV12]  Option A is losing $0.25 per month x 12 months = $3.00 gained over the year.  OPTION B: [FV1 = $265.04] + [FV2 = $264.40] + [FV3 = $263.76] + [FV4] + … + [FV24]  Option B is losing $0.64 every half-month x 24 half-months = $15.36 gained over the year.  Overall, Option B is better

 p. 417 #8, 9, 10, 13