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