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.
7.2 THE CONDITIONS OF AN ANNUITY
Loan Amount $19,000 $19,000 $19,000
Annual Interest Rate
6.5 % 8% 6.5%
Term 3 years 3 years 6 years
Payment Frequency
Monthly Monthly Monthly
Amount Owed at end of Term
$23,078.76 $24,134.50 $28,033.12
Monthly Payments
$641.08 $670.40 $389.35
WHICH INVESTMENT IS BETTER? 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 15th and the 30th of each month) of $250, invested at 5.85% per year, compounded semi-monthly.
WHICH INVESTMENT IS BETTER?
Payment
Frequency Interest Interest Frequency
OPTION A
$500 Monthly 6%/year Compounded monthly
OPTION B
$250 Semi-monthly
5.85%/yr Comp. 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 = 12FV1 = 500(1.005)12 The 1st payment gets interest over 12 months.FV2 = 500(1.005)11 The 2nd payment gets interest over 11 months.FV3 = 500(1.005)10 The 3rd payment gets interest over 10 months, etc.
[FV1 = $503] + [FV2 = $502.75] + [FV3 = $502.50] + [FV4] + … + [FV12]
OPTION B: PV: 250, i = 0.0585/24 = 0.0024375, n = 24FV1 = 250(1.0024375)24 1st payment gets interest over 24 semi-months.FV2 = 250(1.0024375)23 2nd payment gets interest over 23 semi-months.FV3 = 250(1.0024375)22 3rd payment gets interest over 22 semi-months, etc.
[FV1 = $265.04] + [FV2 = $264.40] + [FV3 = $263.76] + [FV4] + … + [FV24]
WHICH INVESTMENT IS BETTER?
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
7.2 HOMEWORK p. 417 #8, 9, 10, 13