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The Power of Compounding

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.

Anyone can take advantage of compound interest simply by opening a savings account.

Definitions:

The principal in financial formulas is the balance upon which interest if paid.

Simple interest is interest paid only on the original principal, and not on any interest added at later dates.

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?

Simple Interest Formula: A = (P)(APR)(Y)

(principal)(annual percentage rate)(number of years)

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.

Now work on Page 243 problems 41 – 44.

Compound Interest

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?

Compound Interest Formula (annually): [pic]

A = accumulated balance after Y years

P = starting principal

APR = annual percentage rate (as a decimal)

Y = number of years

Now work on some more Examples: p. 243-244 problems 47-52

Compound Interest Formula for Interest Paid n times per year

[pic]

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

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.

Now work on some more examples: p. 244 problems 53-60

Continuous Compounding

You deposit $100 in an account with an APR of 8% and continuous compounding. How much will you have after 10 years?

Compound Interest Formula for Continuous Compounding

[pic]

where:

A = accumulated balance after Y years

P = starting principal

APR = annual percentage rate (as a decimal)

Y = number of years

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.

Now work on some more examples: p. 244 problems 65-70

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