Lecture 12Compound Interest

Ana Nora Evans 403 KerchofAnaNEvans@virginia.eduhttp://people.virginia.edu/~ans5k/

Math 1140 Financial Mathematics

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A) I finished homework 5.B) I didn’t start homework 5.C) I got stuck in a problem in homework 5.D) Do we have a homework!?

If you answered C you should come to the office hours.

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Office Hours

Monday 11:00-12:30Tuesday 3:30-5:00 Friday 2:30-3:30 In Ker 403.

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Review Session

It is not required.It will be useful for students that joined the class late and missed the first few classes.It offers the chance to clarify some concepts from the previous classes.

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I am sorry for Sunday. Is Wednesday 7pm working for you?

A) It works and I plan to come.

B) I can come to office hours instead.

C) I would like to come but I have other commitments.

D) I don’t need extra help.

If you answered C please email me to make an appointment or come prepared to ask questions on Friday and Monday.

Review Session

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Questions

About last classAbout homework

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Sample exam 1 postedPractice exercises posted (we will work on them in class on Friday, Sep 23, and Monday, Sep 26).Exam 1 covers sections 1.2 trough 1.9 sections 2.1 trough 2.5 sections 3.1 and 3.2

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Plan for this week

Monday(today) – sections 3.4 and 3.5Wednesday – sections 3.6 and 3.7Friday and Monday(exam review, work in groups on practice problems, class in Rice Hall first floor)

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Last time

Started compound interest.Compound amount formulaPresent value at compound interest

Sections 3.1 and 3.2

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Today

Annual effective rateAnnual effective rate of compound discountCompound rate formula

Sections 3.4 and 3.5

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m is the number of conversion periods per year.

i(m) is the nominal interest rate.

Interest rate per conversion period i = i(m)/m

Nominal Interest Rate and Interest Rate

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Compound amount formula is S = P(1+i)n

where

n is the total number of conversion periods

P is the principal

S is the amount

i is the interest rate per conversion period

Present value formula at compound interest is

P = S(1+i)-n

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Obsetvation

n, the total number of conversion periods is a natural number.For any fractions of a conversion period, use simple interest formula.E.g., after calculations you end up with 3.5 conversion periods then the amount is S = (P(1+i)3)(1 + 0.5 x i)

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Questions?

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Suppose that a savings account pays 3% interest per quarter compounded quarterly. If $2,500 is deposited, how much is in the account 5 years later?

A) 2,500(1+0.03/4)-5

B) 2,500(1+0.03)-20

C) 2,500(1+0.03/4)5

D) 2,500(1+0.03)20

E) I don’t know

Pledged Question

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Suppose that a savings account pays 3% interest per quarter compounded quarterly. If $2,500 is deposited, how much is in the account 5 years later?

Answer

The interest rate is given as interest rate per conversion period, thus i = 3%. Since there are 4 conversion periods per year and the term is 5 years, then n = 20. The principal is P=$2,500. The correct answer is 2,500(1+0.03)20

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Google Group

I created a google group for this class FinMathFall2011. You must join the group to receive class emails. The 13 students did not join are doing it at their own risk.One of the messages on the group list tells you how to subscribe for updates of the class website.

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Emails

To receive my emails you must whitelist my email addresses:AnaNEvans@gmail.comAnaNEvans@virginia.eduans5k@virginia.edu

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Warning

From now on you are responsible for any emails sent to your UVa email address and to the FinMathFall2011 google group.

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Annual Effective Rate

Given a nominal interest rate i(m), the annual effective rate is the interest rate i such that if the same principal P is deposited in two accounts: one with nominal interest rate i(m) and one with yearly interest rate i, compounded yearly; at the end of one year the two accounts have the same balance.

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The compounded amount formula is S = P(1+i)n

The balance in an account with nominal interest rate i(m) after one year is:

S = P(1 + i(m)/m)m

The balance in an account with interest rate i per year, compounded yearly, after one year is

S = P(1 + i)1

To calculate i

P(1 + i) = P(1 + i(m)/m)m

i = (1 + i(m)/m)m - 1

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Why does one calculate annual effective rate?

It allows us to compare different nominal interest rates.

You are considering two different savings accounts. The first pays 4.7% compounded monthly and the second one pays 4.63% compounded daily. Which one is the better deal?

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You are considering two different savings accounts. The first pays 4.7% compounded monthly and the second one pays 4.63% compounded daily. Which one is the better deal?

The annual effective rate formula is

1+i = (1 + i(m)/m)m

For the first account:

For the second account:

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Wednesday

Homework 5 due

Read sections 3.4, 3.5,

3.6, 3.7

Friday and Monday

Exam 1 review

First Exam (max 15 points):

26 September 2011 at 7pm

in CLK 108

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