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Section3.34 - Discounted Value of An Ordinary Simple...

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Discounted Value of An Ordinary Simple Annuity (section 3.3) Consider the following An ordinary simple annuity consisting of n -payments of $1 we wish to determine the present value, A , of these payments at the beginning of the term that is, what is the present value one interest period before the first payment is due to be made?
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We denote the above sum by the symbol i n a | (read: a -angle- n -at- i ) i n a | = i i n - + - ) 1 ( 1 This is called the discount factor for n -payments
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Notes 1. If the ordinary simple annuity consisted of n -payments of $ R , then the discounted or present value is: S = R i n a | = R i i n - + - ) 1 ( 1 2. Relationship between A and S to determine the relationship, let’s draw a time diagram:
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Examples of Where Present Values of Annuities are Used 1. Take out a loan and repay it with periodic payments 2. Invest a sum of money today in order to withdraw payments every period over time 3. You buy an investment that pays $ R every period for n -periods; the price you pay for this investment is: 4. Present values can be used to make a business decision by comparing different financial assets
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Example 3.3.1 You can buy a car for $5000 down and payments of $299 per month for 5 years. The financing rate is j 12 = 9%. What is the equivalent purchase price of the car?
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