Sullivan PreCalculus Section 4.7 Compound Interest

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Presentation transcript:

Sullivan PreCalculus Section 4.7 Compound Interest Objectives of this Section Determine the Future Value of a Lump Sum of Money Calculate Effective Rates of Return Determine the Present Value of a Lump Sum of Money Determine the Time Required to Double or Triple a Lump Sum of Money

Interest is the money paid for the use of money Interest is the money paid for the use of money. The total amount borrowed is called the principal. The rate of interest, expressed as a percent, is the amount charged for the use of the principal for a given period of time, usually on a yearly (per annum) basis.

Simple Interest Formula I = Prt The amount A after t years due to a principal P invested at an annual interest rate r compounded n times per year is

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

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

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 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 10% per annum compounded quarterly?