Lesson28

Lesson28 - Summer Lesson 28 MA 15200, Appendix I Sections...

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1 Summer Lesson 28 MA 15200, Appendix I Sections 5.5 and 5.6 You are familiar with the simple interest formula, I prt = . However, in many accounts the interest is left in the account and earns interest also. We say the account earns compound interest. For example: Suppose Bob invests $100 at 10% simple interest. At the end of 1 year, Bob has earned 100(.10)(1) $10 I == . He now has $110. ( A = P + Prt or A = P(1 +rt )) At the end of the 2 nd year, Bob has earned 110(.10)(1) $11 I = = . He now has $121. At the end of the 3 rd year, Bob has earned 121(.10)(1) $12.10 I = = . He has a total of $143.10. I’m sure you get the idea of what is happening. Formula for Compound Interest with Annual compound interest: (1 ) , where is the initial investment (principal), is the number of years, is the annual interest rate, and is the future value or final value. t SP r P tr S =+ Ex 1: Assume that $1500 is deposited in an account in which interest is compounded annually at a rate of 6%. Find the accumulated amount after 5 years. Ex 2: Assume that $1500 is deposited in an account in which interest is compounded annually for 5 years. Find the accumulated amount, if the interest rate is 8 ½ %. Many banks or financial institutions figure interest more often than once a year; quarterly monthly, semiannually, daily, etc. For example, if the annual rate or nominal rate is 12% and interest is compounded quarterly, that is equivalent to 3% every 3 months. 3% is called the periodic rate .
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2 Formula for Periodic Rate: Periodic Rate = annual rate number of periods per year , where is annual interest rate, is the number of times interest is paid each year, and is the periodic rate.
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Lesson28 - Summer Lesson 28 MA 15200, Appendix I Sections...

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