Exercise 8 Page 351

Compound interest is the interest earned on the principal and on previously earned interest. Let's recall the formula that gives the balance y of an account earning compound interest. y= P( 1+r/n )^(nt) In this formula, P is the principal or initial amount, r is the annual interest rate written in decimal form, t is the time in years, and n is the number of times the interest is compounded in one year. Let's pay close attention to the given exercise.

You deposit $ 500 in an account that earns 6.5 % annual interest compounded yearly.

We can immediately identify P as 500. Also, the annual interest rate, written as a decimal number, is 0.065. Finally, since the interest is compounded yearly, we have that n= 1. Let's substitute these values into the formula and simplify.

y=P( 1+r/n )^(nt)

SubstituteValues

Substitute values

y= 500( 1+0.065/1 )^(1t)

CalcQuot

Calculate quotient

y=500(1+0.065)^(1t)

IdPropMult

Identity Property of Multiplication

y=500(1+0.065)^t

AddTerms

Add terms

y=500(1.065)^t

To graph the function we will make a table of values. Since time is always greater than or equal to 0, we will assign non-negative values for t.

t	500(1.065)^t	y=500(1.065)^t
	500(1.065)^()darkviolet0	500
1	500(1.065)^()darkviolet1	532.5
3	500(1.065)^()darkviolet3	≈ 604
5	500(1.065)^()darkviolet5	≈ 685
10	500(1.065)^()darkviolet10	≈ 939

Let's now plot and connect the obtained points. Since both variables are non-negative, we will only draw in the first quadrant.