Exercise 69 Page 768

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.

$ 500 is deposited in a savings account that earns 5.25 % annual interest compounded annually.

We can immediately identify P as 500. Also, the annual interest rate, written as a decimal number, is 0.0525. Finally, since the interest is compounded annually, 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+0.0525/1 )^(( 1)t)

CalcQuot

Calculate quotient

y=500(1+0.0525)^t

AddTerms

Add terms

y=500(1.0525)^t

To find out the balance after 10 years, we can substitute t=10.

y = 500(1.0525)^t

Substitute

t= 10

y = 500(1.0525)^(10)

UseCalc

Use a calculator

834.048

RoundDec

Round to 0 decimal place(s)

834

We found out that balance after 10 years is 834 dollars.