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Lecture 18Ordinary Annuities
Ana Nora Evans 403 [email protected]://people.virginia.edu/~ans5k/
Math 1140 Financial Mathematics
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2Math 1140 - Financial Mathematics
Grade components
CP is class participation. Maximum 165.HW is homework. Maximum 25.E1 is exam 1. Maximum 100.EC is extra credit and bonus questions. It includes the points for the bonus questions in homework 4, homework 5, and exam 1. Maximum 100.
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3Math 1140 - Financial Mathematics
The exam wasA) Too hardB) HardC) Just about rightD) EasyE) Too easy
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4Math 1140 - Financial Mathematics
Problem 1 a from the study guide b similar to problem 1b in the exam sample c similar to problem 6 from practice problemsProblem 2 a from the study guide and I wrote in HW 5 solutions I will give this on the exam until everybody gets it right b similar to problem 19 from practice problems
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5Math 1140 - Financial Mathematics
Problem 3 similar to problem 4 in the sample examProblem 4 similar to problem 3 in the sample examProblem 5 a) similar to problem 20 in the practice problems b) problem 51 in the practice problemsProblem 6 similar to problem 5 in the sample exam
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6Math 1140 - Financial Mathematics
Problem 7 a) similar to problem 39 in the practice problems b) similar to problem 7 in the practice problemsProblem 8 similar to problem 8 in the sample examProblem 9 similar to problem 9 in the sample exam
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7Math 1140 - Financial Mathematics
Do you feel your exam grade is a good reflection of your efforts in this class?
A) YesB) NoC) I don’t know
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8Math 1140 - Financial Mathematics
Exam 1 grade distribution
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9Math 1140 - Financial Mathematics
Extra credit
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10Math 1140 - Financial Mathematics
Questions
About last classAbout homework
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11Math 1140 - Financial Mathematics
Page 95, #12
How long it will take $1,000 to be worth $1,388 at 8%(2) if:a) You answer to the nearest (rounded) n?b) No interest is given and the worth is at least
$1,388.c) We use simple interest (Banker’s rule) for a part
of a period.
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12Math 1140 - Financial Mathematics
Page 98, #18
A $10,000, 5-year note is sold in 1 year to a person requiring 7(4)%. Find the proceeds.
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13Math 1140 - Financial Mathematics
Last time
Review of compound interest.Solved some homework exercises.
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Math 1140 - Financial Mathematics14
If a<b then a+b<a+c.
If a<b and c<0 then ac>bc.
If a<b and c>0 then ac<bc.
Show x2 ≥ 0
Inequalities
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Math 1140 - Financial Mathematics15
Suppose that you open an investment account with a deposit of $2000.
A year later, you deposit another $2000.
A year after that (two years after the account is opened), you deposit another $2000.
If the investment pays an effective rate of 8%, how much is in the account immediately after the third deposit?
Work on this together for 3-4 minutes.
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Math 1140 - Financial Mathematics16
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Math 1140 - Financial Mathematics17
Suppose that you open an investment account that pays an effective rate of 8%. If you make 40 annual deposits (each on January 1) of $1000 each, how much will be in the account immediately after the 40th deposit?
A) 40 $1,000
B)40 $1,000(1+0.08)
C) $1,000(1+0.08)39 + $1,000(1+0.08)38 + $1,000(1+0.08)37 + ... + $1,000(1+0.08)0
D)$1,000(1+39 0.08) + $1,000(1+38 0.08) + $1,000(1+37 0.08) + ... + $1,000(1+0 0.08)
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Math 1140 - Financial Mathematics18
Suppose that you open an investment account that pays an effective rate of 8%. If you make 40 annual deposits (each on January 1) of $1000 each, how much will be in the account immediately after the 40th deposit?
The correct answer is C.
If you answered A, then you forgot about the interest. You considered the interest rate to be zero.
If you answered B, then you considered the interest for only one conversion period.
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Math 1140 - Financial Mathematics19
How do we calculate: $1,000(1+0.08)39 + $1,000(1+0.08)38 + $1,000(1+0.08)37 + ... + $1,000(1+0.08)0 ?
$1,000[(1+0.08)39 + (1+0.08)38 + (1+0.08)37 + ... + (1+0.08)0]
(1.08)39 + (1.08)38 + (1.08)37 + ... + (1.08)0
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20Math 1140 - Financial Mathematics
Geometric Series
S = xn + xn-1 + … + x + 1
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Math 1140 - Financial Mathematics21
Suppose that R dollars are deposited at equally spaced times in an account paying interest of i percent per time period, compounded once per period.
If n such deposits are made, then immediately after the nth deposit the account balance S is
i
iRS
n 1)1(
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Math 1140 - Financial Mathematics22
Wednesday
Homework 6 due
Read sections 4.1 and 4.2
Project Teams due next Friday.
Charge