Compound Interest

1. Compound Interest If a principal amount P is invested at a compound interest rate i per interest period for a total of n interest periods, then the compound amount A at the end of the nth period is given byA = P(1 + i)n

2. If interest is compounded for t years with m interest periods each year, there will be a total of mt interest periods if we replace n by mt and replace i by rm, we obtain the formula A = P(1 + r/m)mt where P = principal amountr = interest rate per yearm = number of interest periods per yeart = number of years

3. Suppose that $5000 is invested at 8% per year, with interest compounded annually. What is the compound amount after 3 years?

4. P = 5000 i = .08 n = 3 A = P(1+i)n A= 5000(1+.08)3 A= 6298.56 dollars

5. Suppose that $1000 is deposited in a savings account that pays 6% per annum, compounded quarterly. If no additional deposits or withdrawals are made, how much will be in the account at the end of 1 year?

6. P = 1000 r = .06 m = 4 t = 1

7. 0.6 Functions and Graphs in Applications

8. Solving application problems • Draw a picture to help visualize the problem. • Label known quantities in the picture. • Determine the equation(s) for the problem using the known quantities. • Solve the equation(s) for the desired quantities.

9. Assign letters to the dimensions of the rectangle. The height of the rectangleis three times its width. 3W W

10. Consider the Norman window below. • Write an expression for its perimeter. • Write an expression expressing the fact that its area is 2.5 square meters. P = 2x + y + πy P = 2x +(1+ π)y y x