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6.7 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 on theme: "6.7 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."— Presentation transcript:

1 6.7 Compound Interest

2 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.

3 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

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 (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 …

6 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?

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11 Graphing Solution Solve the equation The x-coordinate of their point of intersection is the time t of how long till the investment doubles. Graph both functions. Using INTERSECT command we find x =

12 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.


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