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Chapter 6 Section 3 Gabby Prezkop Period 7 Compound Interest • Compound interest is the total amount of an investment, A, earning compound interest is: • A(t)=P(1+r/n)nt • Where P is the principal , r, is the annual interest rate, n, is the number of times interest is compounded per year & t is the time in years. • Annual is compounded 1 a year. • Quarterly is compounded 4 times a year. • Monthly is compounded 12 times a year. Once every month. • Daily is compounded 365 times a year. Once a day. Examples • Suppose Karen has $1000 that she invests in an account that pays 3.5% interest compounded quarterly. How much money does Karen have at the end of 5 years? • How to Solve: • You first plug $1000 in for the principal because that is the amount that she invested. • A= 1000(1+r/n)nt How to: Next, put the 3.5% interest rate in for r as a decimal. And plug in four for n because its compounded quarterly. Lastly, plug a 5 in for t because it’s the amount compounded after 5 years. A=1000(1+.035/4)4(5) And use the order of operations to solve! • Problem 1) If you have a bank account whose principal = $1000, and your bank compounds the interest twice a year at an interest rate of 5%, how much money do you have in your account at the year's end? • Problem 2) If you start a bank account with $10,000 and your bank compounds the interest quarterly at an interest rate of 8%, how much money do you have at the years end ? (assume that you do not add or withdraw any money from the account) • Problem 1: A=1000(1+.05/2)2(1) A=$1050.63 Problem 2: A= 10000(1+.08/4)4(1) A=$10824.32 Effective Yield • Effective yield is annually compounded interest rate that yields the final amount of an investment.
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