Chapter 6 Class Notes
Simple interest vs. Compound interest: o Simple interest amount = Principal * annual interest rate * period o Compound interest amount includes interest not only on the initial investment but also on the accumulated interest in previous periods. Example: Assume we will save $1,000 for three years and earn 6% interest compounded annually.
Original balance First year interest Balance, end of year 1 Balance, beginning of year 2 Second year interest Balance, end of year 2 Balance, beginning of year 3 Third year interest Balance, end of year 3 $ 1,000.00 60.00 $ 1,060.00 $ 1,060.00 63.60 $ 1,123.60 $ 1,123.60 67.42 $ 1,191.02

Time value of Money: 1. A single sum:
Assume we will save $1,000 for three years and earn 6% interest compounded annually. On 1/1 in Year 1: $1,000 on Dec. 31 in Year3: $ 1,191.02

(a) Future value of a single sum = Present value * (1+ r) n Future value of $1000 after 3 years: 3 $1,000 × [1.06] = $1,191.02 (b) Present value of a single sum = Future value *( 1/ (1+ r) n ) Present value of $1,192.02: 3 $1,191.02 × (1/ [1.06] )= $1,000
Where r = interest rate n= compounding periods

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Example: Assume you plan to buy a new car in 5 years and you think it will cost $20,000 at that time. What amount must you invest today in order to accumulate $20,000 in 5 years, if you can earn 8% interest compounded annually? i = .08, n = 5 Present Value Factor = .68058

$20,000 × .68058 = $13,611.60 If you deposit $13,611.60 now, at 8% annual interest, you will have $20,000 at the end of 5 years.

2. An annuity: An annuity is a series of equal periodic payments
(a) An ordinary annuity: An annuity with payments at the end of the period. (b) An “Annuity Due”: An annuity with payments at the beginning of the period.

Future value of an annuity:
Example 1 (An ordinary annuity): We plan to invest $2,500 at the end of each of the