<p> The Power of Compounding</p><p>On July 18, 1461, King Edward IV of England borrowed the modern equivalent of $384 from New College of Oxford. The King soon paid back $160, but never repaid the remaining $224. The debt was forgotten for 535 years. Upon its rediscovery in 1996, a New College administrator wrote to the Queen of England asking her repayment, with interest. Assuming an interest rate of 4% per year, he calculated that the college was owed $290 billion. This example illustrates the power of compounding (how amazing money can grow over time), which is the main focus of this section of Chapter 4.</p><p>Anyone can take advantage of compound interest simply by opening a savings account.</p><p>Definitions:</p><p>The principal in financial formulas is the balance upon which interest if paid.</p><p>Simple interest is interest paid only on the original principal, and not on any interest added at later dates.</p><p>Compound interest is interest paid both on the original principal and on all interest that has been added to the original principal. Simple Interest Imagine that you deposit $1,000 in Honest John’s Money Holding Service, which promises to pay 5% interest each year. How much money do you have after three years?</p><p>Simple Interest Formula: A = (P)(APR)(Y) (principal)(annual percentage rate)(number of years) </p><p>Your original $1,000 has grown in value to ______. Honest John’s method of payment represents simple interest, in which interest is paid only on your actual investment, or principal. </p><p>Now work on Page 243 problems 41 – 44. Compound Interest</p><p>Now, suppose that you place the $1,000 in a bank account that pays the same 5% interest once a year. But instead of paying the interest directly, the bank adds the interest into your account. How much is your balance at the end of the three years under this method?</p><p>Compound Interest Formula (annually): A  P (1 APR) Y</p><p>A = accumulated balance after Y years P = starting principal APR = annual percentage rate (as a decimal) Y = number of years</p><p>Now work on some more Examples: p. 243-244 problems 47-52 Compound Interest Formula for Interest Paid n times per year</p><p>APR A  P (1 )(nY ) n where: A = accumulated balance after Y years P = starting principal APR = annual percentage rate (as a decimal) n = number of compounding periods per year Y = number of years</p><p>Example: You deposit $5,000 in a bank account that pays an APR of 3% and compounds interest monthly. How much money will you have after 5 years? Compare this amount to the amount you would have if interest were paid only once a year.</p><p>Now work on some more examples: p. 244 problems 53-60 Continuous Compounding</p><p>You deposit $100 in an account with an APR of 8% and continuous compounding. How much will you have after 10 years?</p><p>Compound Interest Formula for Continuous Compounding</p><p>A  P e( APRY ) where: A = accumulated balance after Y years P = starting principal APR = annual percentage rate (as a decimal) Y = number of years</p><p>The number e is a special irrational number with a value of e = 2.71828 (approx.). You compute e to a power with the ex key on your calculator. </p><p>Now work on some more examples: p. 244 problems 65-70</p>