Financial Mathematics I

Week 8

• Start on stage 3 of final project.– Paper copy is due week 10 (include all

stages, including before and after revisions).– Presentations are week 10.

• Revised stage 2 is due next week.

Some problems to review what we’ve been learning.

A CPI problemIn 2006 (CPI: 201.6), UIC’s tuition was $3,123 per

semester. In 2007 (CPI: 207.3) was $3,341 per semester. When was it more “expensive”?

201.6 = 3123 207.3 x

x = $3211.30 (2006’s tuition in 2007 constant dollar value)

It was more “expensive” in 2007.

Some problems to review what we’ve been learning.

Some Percentage problemsa) Making $55,000 now. Have to take a 5% pay cut for next

year or leave the job. How much am I making next year?

x = 55,000 * (1 – 0.05) = $52,250

b) A town has a population of 1050 in the year 2005. This represents a 26% increase since 1980. What was the population in 1980?

1050 = x * (1 + .26) x = 833 people

Some problems to review what we’ve been learning.

A Compound percentage problem

Shoes go on a 15% sale. Then from the sale price, it is marked up 10%. If the final price was $35, what was the original price?

x * (1 - .15) (1 + .1) = 35

x * .85 * 1.1 = 35

x * .935 = 35

x = $37.43

• This Week: Savings account

• Next Week: Mortgage, school loans

• In 2 Weeks: Project Presentations

Savings Account

A. Simple interest: I = Prtinterest = principal * rate * time

e.g. If you made a deposit of $3,500 in an account that pays 8.4% interest, how much will you have after 7 years?

interest = 3,500 * .084 * 7 = 2058$2058 + $3,500 = $5558

But this is not the way banks do it!

Savings Account

B. Compound interest:

A= final balanceP= principalr= raten= # of times compounded per yeart= # of years

1nt

rA P

n

e.g. You deposit $4000 in an account that pays 2.92% annual interest. Find the balance after 3 years if interest is compounded quarterly?

A= 4000 * (1 +.0292/4)^(4*3)

= $4364.82

How about if it’s compounded monthly?

A= 4000 * (1 +.0292/12)^(12*3)

= $4365.74

Comparing Compound Interest

You deposit $2200 in a bank account. Find the balance after 4 years if the account pays 3.2% interest – compounded quarterly– monthly– daily

Let’s do this together on Excel.

Comparing Compound Interest

Comparing Compound Interest

Comparing Compound Interest

Comparing Compound Interest

Comparing Compound Interest

Comparing Compound Interest

APY

Annual Percentage Yield – yield you earn on a deposit over a year.

Make sure to take note of this when choosing a bank for a savings account. It’s different from the annual interest rate.

Go back to the excel file just made and calculate the APY for each of those options. APY is the percentage change for one year.

APY

APY

Example 1

You deposit $3,000 in an account that compounds monthly at 5.6% annual interest. Use Excel to determine how long it takes for your money to double.

Example 1

Example 2

You’re trying to save up $7000 within 10 years. If you put your money into an account that compounds quarterly at 5.4% annual interest, what is the minimum initial deposit?

Example 2

7000 = P (1 + .054/4)^(4*10)7000 = P (1.70982)P = $4094.00

Or, if you used Excel…

Start with some number as your initial balance.

Example 3

You’re trying to save up $7000 in an account for 10 years that compounds monthly with initial deposit of $6400. What is the minimum annual interest you are looking for?

Example 3

7000 = 6400 * (1 + r/12) ^ (12*10)

7000/6400 = (1 + r/12) ^ 120

1.09375 = (1 + r/12) ^ 120

1.09375 ^ (1/120) = (1 + r/12)

1.000747 = 1 + r/12

r/12 = 0.000747

r = 12 * 0.000747 = .00896 = 0.90%

Today: lab 12

Homework:

Revise part 2 of the Project

Start working on part 3 of the Project

Extra Credit: Assignment 6 (I’ll replace your lowest assignment grade with this grade.)