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
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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
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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 .
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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
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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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