Chapter 9.2, Problem 43E

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Annuities If an annuity can make an unending number of equal payments at the end of the interest periods, it is called a perpetuity. If a lump sum investment of A n is needed to result in n periodic payments of R when the interest rate per period is i, then A n = R [ 1 − ( 1 + i ) − n i ] (a) Evaluate lim n → ∞ A n to find a formula for the lump sum payment for a perpetuity.(b) Find the lump sum investment needed to make payments of $100 per month in perpetuity if interest is 12% compounded monthly. (a) To determine To calculate: The value of the limit, limnAn where An=R[1(1+i)ni], is discontinuous at any value of x, where x is the advertising expenditure, in thousands of dollars, and y is the sales volume. Explanation Given Information: The investment needed to result in n periodic payments of R with interest rate i, is represented by, An=R[1(1+i)ni]. Formula used: A limit limxcx can be simplified as, limxcx=c Calculation: Consider the provided function, An=R[1(1+i)ni] Consider the provided limit, limnR[11 (b) To determine To calculate: The lump sum investment required for making the payments$100 per month in perpetuity for an interest rate of 12% compounded monthly.

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