Exercise 12 Page 869

We deposit $500 into an account paying 4.5 % interest compounded semiannually. We want to find the value of the account after 10 years. Our account earns compound interest, which means that interest is earned not only on the $500 we deposited but also on any earned interest. Let's recall the formula that gives the balance y of an account earning compound interest. y= P( 1+r/n )^(n t)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 scenario.

We can immediately identify P as 500. Also, the interest rate, written as a decimal number, is 0.045. Since the interest is compounded semiannually, or 2 times a year, we have that n= 2. Finally, we want to find the value of the account after 10 years, so t = 10. Let's substitute these values into the formula and evaluate.

The value of the account after 10 years rounded to the nearest penny is $ 780.25.