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6.7 Compound Interest

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**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)

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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

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**Continuous Compounding**

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

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**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

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**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?

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**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

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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.?

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

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

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**Graph What is the value of y for x = 10?**

Describe the behavior of the graph.

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