1. LEQ: How do you calculate compound interest?

2.  Suppose you deposit $2,000 in a bank that pays interest at an annual rate of 4%. If no money is added or withdrawn, after one year the account will have the original amount invested, plus 4% interest.  After one year: 2000 +.04(2000) = 2000(1 +.04) = 2000(1.04) = 2080  There will be $2,080 in the bank after one year.  Notice that to find the amount after one year, you do not have to add the interest; you can just multiply by 1.04.

3.  Similarly, at the end of the second year, there will be 1.04 times the amount after the first year.  Amount after 2 years: 2000(1.04)(1.04) = 2000(1.04) 2 = 2163.20  There will be $2,163.20 in the bank after 2 years.  Amount after 3 years: 2000(1.04)(1.04)(1.04) = 2000(1.04) 3 = 2249.73 There will be $2,249.73 in the bank after 3 years. Amount after t years: 2000(1.04) t

4.  Because the interest earns interest each year, the process is called compounding.  Annual Compound Interest Formula:  Let P be the amount of money invested at an annual interest rate of r compound annually. Let A be the total amount after t years. Then A = P(1 + r) t  A is the amount in the account after t years  P is the principal…initial invested  r is the annual interest rate as a decimal  t is the number of years the money was invested (going back in time…negative value of t)

5.  Sally has invested $4,000 in an account with an annual interest rate of 6.2%. If she leaves the interest in the account, how much will she have after 4 years?  P = 4000  r =.062  t = 4  A = 4000(1 +.062) 4  A = 4000(1.062) 4  A = 4000(1.27203)  A = 5088.12  She will have $5,088.12 after 4 years.

6.  Semi-annually: 2 times a year  Quarterly: 4 times a year  Monthly: 12 times a year  Daily: 365 times a year  General Compound Interest Formula:  Let P be the amount invested at an annual interest rate r compounded n times per year. Let A be the amount after t years. Then

7.  Bill put $2,500 in a 5-year CD (certificate of deposit) that pays 7.4% compounded quarterly. How much will the CD be worth when it matures?  P = 2500  r =.074  n = 4  t = 5  The CD will be worth $3,607.12 when it matures.

8.  The rate of interest earned after all the compoundings have taken place in one year.  Find the amount of interest $1 would earn in the account in one year.  For example: Find the effective annual yield of an account paying 5.25% interest compounded monthly.  So the interest earned is $1.05378 - $1 = $.05378  Thus a rate of 5.25% compounded monthly gives an effective annual yield of 5.378%.

9.  Lesson Master 7-4A #1, 2

10.  Pgs. 441-443 #1-3, 6-16, 20-25