Lecture_7._Compound_Interest

Lecture_7._Compound_Interest - 1 LECTURE 7 Compound Interest

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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´µµµ ORDQ IRU ³ \HDUV DW ·¸ 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
3-5 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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3-8 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?

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This note was uploaded on 08/10/2011 for the course ECON 123 taught by Professor Other during the Spring '11 term at Pontificia Universidad Catolica Madre y Maestra.

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Lecture_7._Compound_Interest - 1 LECTURE 7 Compound Interest

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