Math 221 Intro to Algebra Week 4 DQ 1

5

Using the power rules with integral exponents

Simplify. Write answers without negative exponents. Assume that the variables represent nonzero real numbers.

Solution

Now do Exercises 47–62

Calculator Close-Up

You can use a calculator to demonstrate that the power of a power rule for exponents holds when the exponents are negative integers.

3 The Present Value Formula

In Section 4.1, we studied the amount formula A = P(1 + r)n. If we are interested in the principal P that must be invested today to grow to a specified amount A in the future, then the principal is called the present value of the investment. We can find a formula for present value by solving the amount formula for P:

Present Value Formula

The present value P that will amount to A dollars after n years with interest compounded annually at annual interest rate r is given by the formula

EXAMPLE 6

Using the present value formula

A new parent wants to have $20,000 in his child's college fund when his infant is ready for college in 18 years. How much must he invest now at 8% compounded annually to achieve this goal?

Solution

Use n = 18, A = $20,000, and r = 0.08 in the present value formula:

An investment today of $5004.98 will amount to $20,000 in 18 years.