finite mathematics: an applied approach by michael sullivan copyright 2011 by john wiley & sons....

Finite Mathematics: An Applied Approach by Michael SullivanCopyright 2011 by John Wiley & Sons. All rights reserved.

6.4 Present Value of an Annuity; Amortization



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The present value of an annuity is the amount that must be deposited today (at the same compounded interest rate as the annuity) to provide all the payments for the term of the annuity.


Finding the Present Value of an Annuity

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We seek a formula for the present value of an annuity

……..


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Theorem

Present Value of an Annuity

Suppose an annuity earns interest at the rate of i per payment period. If n withdrawals of $P are made at each payment period, the amount V required is

Here V is called the present value of the annuity.

P is the payment at the end of each periodi is the interest rate per periodn is the number of periods

Present Value of an Annuity

Suppose an annuity earns interest at the rate of i per payment period. If n withdrawals of $P are made at each payment period, the amount V required is

Here V is called the present value of the annuity.

P is the payment at the end of each periodi is the interest rate per periodn is the number of periods

1 (1 ) niV P

i



Getting By in College

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Determining the Cost of a Car

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Lease or Purchase

(a) Which alternative is preferable if the company can invest money at 5% per annum?(b) Which alternative is preferable if the company can invest money at 15% per annum?

(b) 41 (1 ) 1 (1 0.15)

1000 1000(2.85498) $2854.980.15

niV P

i

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A loan with a fixed rate of interest is said to be amortized if both principal and interest are paid by a sequence of equal payments made over equal periods of time.(The Latin word mort means “death.” Paying off a loan is regarded as “killing” it.)

A loan with a fixed rate of interest is said to be amortized if both principal and interest are paid by a sequence of equal payments made over equal periods of time.(The Latin word mort means “death.” Paying off a loan is regarded as “killing” it.)



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Theorem

Amortization

The payment P required to pay off a loan of V dollars borrowed for n payment periods at a rate of interest i per payment period is

Amortization

The payment P required to pay off a loan of V dollars borrowed for n payment periods at a rate of interest i per payment period is

1 (1 ) n

iP V

i



Finding the Payment for an Amortized Loan

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Home Mortgage Payments

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Amortization Table

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finite mathematics: an applied approach by michael sullivan copyright 2011 by john wiley & sons....

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