1. 4.6 Compound Interest

2. Simple Interest. I=Prt A = P+ I = P+Prt = P(1+rt)
If a principal of P dollars is borrowed for a period of t years at a per annum interest rate r, expressed in decimals, the interest I charged is
I=Prt
Amount after t years is
A = P+ I = P+Prt = P(1+rt)

3. Compound Interest
The amount A after t years due to a principal P invested at an annual interest rate r compounded n times per year is

4. Continuous Compounding
The amount A after t years due to a principal P invested at an annual interest rate r compounded continuously is

5. Suppose your bank pays 4% interest per annum
Suppose your bank pays 4% interest per annum. If $500 is deposited, how much will you have after 3 years if interest is compounded …
(a) Annually
(b) Monthly

6. Suppose your bank pays 4% interest per annum
Suppose your bank pays 4% interest per annum. If $500 is deposited, how much will you have after 3 years if interest is compounded continuously?

7. Present Value Formulas
The present value P of A dollars to be received after t years, assuming a per annum interest rate r compounded n times per year, is
If the interest is compounded continuously, then

8. How much should you deposit today in order to have $20,000 in three years if you can earn 6% compounded monthly from a bank C.D.?

9. How long will it take to double an investment earning 6% per annum compounded quarterly?

11. Graph What is the value of y for x = 10?
Describe the behavior of the graph.