6.6 Compound Interest. 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.

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Presentation transcript:

6.6 Compound Interest

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) Simple 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 Compound Interest

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

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

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?

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

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.?

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

Graph What is the value of y for x = 10? What is the value of y for x = 20? Describe the behavior of the graph.