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Lecture_7._Compound_Interest

# Lecture_7._Compound_Interest - 1 LECTURE 7 Compound...

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LECTURE 7 Compound Interest Osvaldo Lagares, M.S. 1

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2 Chapter Outline Compound Interest: The Basics Compounding Frequencies Effective Interest Rates Comparing Effective and Nominal Rates
3

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4 Compound Interest: The Basics /HW¶V FRQVLGHU D ±²³´´´ ORDQ IRU ² \HDUV DW µ· VLPSOH interest. We can easily calculate the simple interest: I = PRT I = \$5,000 x 8% x 5 I = \$2,000 Maturity Value = \$7,000 +RZ GRHV WKH DPRXQW RI LQWHUHVW JURZ RYHU WKH ORDQ¶V term? Year Interest Balance Start N/A \$5,000 Year 1 \$400 \$5,400 Year 2 \$400 \$5,800 Year 3 \$400 \$6,200 Year 4 \$400 \$6,600 Year 5 \$400 \$7,000
3-ː5 Compound Interest: The Basics Now imagine that this is a deposit that you have made in a bank certificate. At the end of the first year, you would have \$5,400 in your account. By leaving it on deposit at the bank for the second year, you are in effect loaning the bank \$5,400. Yet, you are being paid interest only on your original \$5,000. 7KDW¶V how simple interest works. No matter how long the loan continues, under simple interest the borrower pays (and lender receives) interest only on the original principal.

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6 Compound Interest: The Basics This GRHVQ¶W seem quite fair. It seems reasonable that you should receive interest on the entire amount of your account balance. If the bank has the use of \$5,400 of your money in year 2, then you have every reason to expect that it should pay you interest on the full amount, \$5,400. In other words, you want to receive interest on your accumulated interest. That is precisely the point of compound interest . With compound interest , interest is paid on both the original principal and on any interest that accumulates along the way. When interest is paid on interest, we say that it compounds .
7 Compound Interest: The Basics Suppose that we look at the account balance year by year, assuming that interest is credited to the account annually. Year 1 I = PRT I = \$5,000 x 8% x 1 = \$400 Year 2 I = \$5,400 x 8% x 1 = \$432 Year 3 I = \$5,832 x 8% x 1 = \$466.56

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3-ː8 Compound Interest: The Basics SIMPLE INTEREST COMPOUND INTEREST Year Start Interest End Start Interest End Difference 1 \$5,000 \$400 \$5,400 \$5,000 \$400 \$5,400 \$0 2 \$5,400 \$400 \$5,800 \$5,400 \$432 \$5,832 \$32 3 \$5,800 \$400 \$6,200 \$5,832 \$466.56 \$6,298.56 \$98.56 4 \$6,200 \$400 \$6,600 \$6,298 \$503.88 \$6,802.44 \$202.44 5 \$6,600 \$400 \$7,000 \$6,802.44 \$544.20 \$7,346.64 \$346.64 8
9 Compound Interest: The Basics Looking at things year by year is a good way to get a sense of how compound interest works, but a tedious and impractical way of doing an actual calculation. Note that 8% interest for a single year on \$1 amounts to exactly 8 cents. Therefore, in 1 year \$1 turns into \$1.08. What happens to \$5,000? End of year 1 balance \$5,000 x \$1.08 = \$5,400 End of year 2 balance \$5,000 x \$1.08 x \$1.08 = \$5,832 End of year 5 balance \$5,000 x \$1.08 x \$1.08 x \$1.08 x \$1.08 x \$1.08 = \$7,346.64

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10 Compound Interest: The Basics This approach is far more efficient than building an entire table, yet the repeated multiplications are still tedious.
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Lecture_7._Compound_Interest - 1 LECTURE 7 Compound...

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