1. Compound Interest 8.2 Part 2

2. Compound Interest A = final amount P = principal (initial amount) r = annual interest rate (as a decimal) n = number of times compounded per year t = number of years

3. Example 1: Write an exponential equation to model the growth function in the situation and then solve the problem. Suppose you invested $1000 at 5% interest compounded annually (once per year). How much will you have in 10 years? A = final amount P = principal (start) = 1000 r = annual interest rate = 5% n = number of times compounded per year = 1 t = number of years = 10

4. Example 1: Write an exponential equation to model the growth function in the situation and then solve the problem. Suppose you invested $1000 at 5% interest compounded annually (once per year). How much will you have in 10 years? A = 1628.895 = $1628.90

5. Number of times compounded: Annually: n = 1 Bi-annually: n = 2 Quarterly: n = 4 Monthly: n = 12 Weekly: n = 52 Daily: n = 365

6. Example 2: Write an exponential equation to model the growth function in the situation and then solve the problem. Suppose you invested the same $1000 at 5% interest, but instead of annually the interest is compounded quarterly (4 times a year)? Now how much will you have in 10 years? A = final amount P = principal (start) = 1000 r = annual interest rate = 5% n = number of times compounded per year = 4 t = number of years = 10

7. Example 2: Write an exponential equation to model the growth function in the situation and then solve the problem. Suppose you invested the same $1000 at 5% interest, but instead of annually the interest is compounded quarterly (4 times a year)? Now how much will you have in 10 years? A = 1643.619 = $1643.62 Compounded annually: $1628.90

8. Example 3: Write an exponential equation to model the growth function in the situation and then solve the problem. Suppose you invested the $1000 at 5% interest, but now your interest is compounded daily. How much will you have in 10 years? A = final amount P = principal (start) = 1000 r = annual interest rate = 5% n = number of times compounded per year = 365 t = number of years = 10

9. Example 3: Write an exponential equation to model the growth function in the situation and then solve the problem. Suppose you invested the $1000 at 5% interest, but now your interest is compounded daily. How much will you have in 10 years? A = 1648.665 = $1648.67 Compounded quarterly: $1643.62

10. Solve the following problems on a separate piece of paper. Set up the equation first! You may work with ONE other person. When you finish, you may turn in your work. You may use a calculator. 1)Suppose you invested $2000 at 6% interest, compounded monthly. How much will you have in 10 years? 2)Suppose you invested $500 at 4% interest, compounded bi-annually. How much will you have in 25 years?

11. Homework: page 370-372 (2-14 evens, 19-21 all, 31-34 all)