   Chapter 13.4, Problem 29E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# DISCOVER: Present Value of an Annuity(a) Draw a timeline as in Example 1 to show that the present value of an annuity is the sum of the present values of each payment, that is, A p = R 1 + i + R ( 1 + i ) 2 + R ( 1 + i ) 3 + ⋯ + R ( 1 + i ) n (b) Use part (a) to derive the formula for A p given in the text.

To determine

(a)

To show:

The present value of an annuity is the sum of the present values of each payment, that is,

Ap=R1+i+R(1+i)2+R(1+i)3++R(1+i)n

Explanation

Given:

Timeline for individual payments.

Approach:

Present value of an annuity Ap is given by

Ap=Af(1+i)n (1)

Af is the amount of an annuity,

i is the interest per time period and

n is the total number of installments.

Calculation:

Substitute,

Af=R+R(1+i)+R(1+i)2++R(1+i)n1 in equation (1),

Ap=Af(1+i)n=(R+R(1+i)+R(1+i)2+

To determine

(b)

The formula for Ap.

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