Lecture 18 Ordinary Annuities Ana Nora Evans 403 Kerchof [email protected] ans5k/ Math 1140 Financial Mathematics

Lecture 18Ordinary Annuities

Ana Nora Evans 403 [email protected]://people.virginia.edu/~ans5k/

Math 1140 Financial Mathematics

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.


The exam wasA) Too hardB) HardC) Just about rightD) EasyE) Too easy


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


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


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


Do you feel your exam grade is a good reflection of your efforts in this class?

A) YesB) NoC) I don’t know


Exam 1 grade distribution


Extra credit


Questions

About last classAbout homework


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.


Page 98, #18

A $10,000, 5-year note is sold in 1 year to a person requiring 7(4)%. Find the proceeds.


Last time

Review of compound interest.Solved some homework exercises.

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


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.



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)


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.


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


Geometric Series

S = xn + xn-1 + … + x + 1


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(


Wednesday

Homework 6 due

Read sections 4.1 and 4.2

Project Teams due next Friday.

Charge

Documents

Lecture 18 Ordinary Annuities Ana Nora Evans 403 Kerchof [email protected] ans5k/ Math 1140 Financial Mathematics