Math 11
Unit 7 - Finances
Unit Notes Package
GENERAL OUTLINE FOR FINANCES UNIT:
1. Compound Interest/TVM Solver
Assigned work: Finance worksheet #1-20 odds
2. Debts/Loans
Assigned work: Finance worksheet #1-20 evens
3. Real Estate: Housing
Assigned work: Finance worksheet #21-42 odds, find: 3 possible homes (websearch #1)
4. Budgeting/Investments
Assigned work: Finance worksheet #21-42 evens, find: mortgage and investment rate
(websearch #2 - using bank websites)
5. Real Estate: Home Stress Test
Assigned work: Complete Worksheet 1: Home Purchase
6. Car Purchase: Part 1
Assigned work: Find: 2 possible different cars, car loan rate, consumer reports (would
do in real life but SKIP for assignment). Calculate: depreciation on each car using VMR,
true total cost of car after 5 years using financial charge, and the total real cost
(websearch #3 and 4 – find two cars and find car loan rates – Worksheet 2 has a site)
7. Car Purchase: Part 2
Assigned work: Complete Worksheet 2: Car Purchase
8. Opportunity Costs/Investments
Assigned work: Complete Worksheet 3: Investments/Retirement Planning
9. Lab Day 1
Assigned work: Complete 3 budget excel sheets/begin finalizing project
10. Lab Day 2
Assigned work: Finalize project
NOTE TO STUDENTS:
 You have 4 internet searches that must be done after the first class. See bolded searches
above.
 MAKE sure these are printed BEFORE Class so you can bring in your printed forms to work
with in class.
 Make sure to bookmark your sources as well so you have them when submitting the final
project.
 You project includes the submission of the assigned questions 1-43 and Worksheets 1-3.
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
Lesson 1: Compound Interest/TVM Solver
Definitions
TVM Solver:
Inflation rate:
Financial Charge:
Review:
r
A  P(1  ) nx
x
A: Future Value
P: Present Value
r: Rate
n: Time
x: Compounds/year
Example 1.
What will a $15 000 investment grow to after 2 years, 38 years
and 40 years if compounded monthly at 10% interest? Calculate the interest
earned for each time period.
a) 2 years
b) 38 years
c) 40 years
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
To discuss: The last 2 years of an investment is where all the growth occurs, as
can be compared with the first 2 years.
Example 2. Calculate the initial amount (present value) for an investment that
grew to $45 000 in 10 years as 8% compounded monthly?
Example 3. How long would it take for $10 000 to grow to $80 000 at 15%
compounded monthly?
Example 4. How long would it take for $100 000 to become $1 000 000 if
compounded semi-annually at 8%?
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
Using the TVM Solver
APPS

1: Finance

1: TVM Solver
N: Total number of payments
I: Interest (In percent form)
PV: Present Value  Money invested = negative
Money borrowed = positive
PMT: Payment per period
FV: Future Value  Money you owe = negative
Money you have = positive
P/Y: Payments per  Year = 1
Month = 12
Week = 52
Day = 365
C/Y: Compounded  Annually = 1
Semi-Annually = 2
Quarterly = 4
Weekly = 52
Daily = 365
END/BEGIN: When payments are made each period. (If it’s not specified,
default to END)
Example 5. A person invests $50/month (at the beginning of the month) for ten years with
an initial deposit of $1000. What is the final amount if interest is compounded annually at
7%?
N:
I:
PV:
PMT:
FV: ____
P/Y:
C/Y:
Matty 2016
Move cursor to variable you
are solving for and hit
ALPHA ENTER.
Math 11
Unit 7 - Finances
Unit Notes Package
Example 6. What is $10 568.10 worth in today’s dollars? Assuming 3% inflation.
Example 7: You borrow $50, 000 to finance a truck. How much do you monthly if the loan is
financed at 6% compounded annually for five years? Calculate the financial charge.
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
Lesson 2: Debt and Loans
Definitions
Appreciation:
Depreciation:
Good Debt:
Bad Debt:
Opportunity Cost:
Amortization:
Consolidating Debt:
Example 1. How much do you think a $30 000 car is worth after 5 years?
Example 2. Calculate the rate of depreciation per year on a $30 000 vehicle that’s lost 40%
of its value over 5 years.
N:
I:
PV:
PMT:
FV: ____
P/Y:
C/Y:
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
Example 3. A new truck costs $50000 and is financed at 2% compounded annually over 5
years. Calculate the financial charge and the actual cost of the car.
(Note: 60% of its value is lost).
N:
I:
PV:
PMT:
FV: ____
P/Y:
C/Y:
ADVICE: Used cars should have approximately 20000 km/year (check carfax to ensure no
rollback). An ideal car is approximately 4-6 year old car with low KM. The majority of the
depreciation will have been lost but the reliability of the car will be good.
Example 4. Find the financial charge for a $500 000 mortgage at 6% compounded annually
for 15, 25, 35 year amortization.
15 years
N
I
PV
PMT
FV
P/Y
C/Y
Total
Cost
Matty 2016
25 years
35 years
Math 11
Unit 7 - Finances
Unit Notes Package
Example 5. Calculate what the $500 000 home will be worth in 25 years if housing
increases 8% annually.
In how many years will a $500 000 home be worth $1 000 000 if housing increases 8%
annually?
Example 6. You want to be debt-free in 5 years. Currently you have:
 Card A (Visa): A balance of $2436.98 with 18.5% compounded daily.
 Card B (Mastercard): A blanace of $3043.26 with 19% compounded daily.
You qualify for a line of credit at 9.6% compounded monthly. Determine how much you will
save by consolidating the loans and paying with the line of credit.
Card A
N
I
PV
PMT
FV
P/Y
C/Y
Matty 2016
Card B
Line of Credit
Math 11
Unit 7 - Finances
Unit Notes Package
Lesson 3: Real Estate
Budgeting for a home:
The size of your mortgage depends on your income. Here’s a general rule of thumb:
Mortgage given = 8 x Gross Income
If you make $40 000 a year  8(40000) = $320 000 mortgage
ASSIGNMENT: From realtor.ca or mls.ca, find three places for tomorrow.
Example 1. For a $500 000 mortgage compounded at 6% annually with amortization of 15
and 25 years, find the monthly payment and the financial charge.
15 yrs
25 yrs
N
I
PV
PMT
FV
P/Y
C/Y
Example 2. Given a $550 000 home ($50 000 down payment, $500 000 mortgage),
calculate:
http://inflationcalculator.ca/british-columbia/
a) The future value for the home after 5 years if there’s an 1.8% annual appreciation.
b) The future value for the home after 10 years if the inflation rate increases to 2.5%.
N:
I:
PV:
PMT:
FV: ____
P/Y:
C/Y:
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
Example 3. How long ago was the $550 000 home worth $375 000 if there’s an 1.8% annual
appreciation.
Example 4. Find the financial charge for 4%, 6% and 12% interest for the previous example
with 25 years amortization. Suppose you are only making monthly payments on your
mortgage which is being compounded yearly.
http://www.ratehub.ca/current-mortgage-rates-british-columbia
4%
N
I
PV
PMT
FV
P/Y
C/Y
Finance
Charge
Matty 2016
6%
12%
Math 11
Unit 7 - Finances
Unit Notes Package
Example 5. Find the monthly payment for a $300 000 condo rental investment with 3%
annual rate for 25 years with 20% down payment.
Suppose the inflation rate become 8% over a 25 year period, how much is your condo now
worth?
http://www.thecondoseller.com/Condo_Listings/page_1689967.html
Compare your calculated real-estate investment with the same investment in the stock
market.
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
Finance Project Unit
Lesson 4: Investments/Budgets
Example 1.
a) Graph a $1000 investment, invested at 8% (compounded annually) over 40 years.
(use 5 yr increments for the graph)
b) Based on the graph, what is the monetary gain from year 0 to year 10 compared
with:
I. Year 20 to year 30
II. Year 30 to year 40
c) Discuss the reason why it is best to invest early in life.
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
Example 2. Calculate the final amount for an investment, invested at 3% compounded
annually after 5 years? 35 years? 40 years? Contributing $500/month.
5 years
35 years
40 years
N
I
PV
PMT
FV
P/Y
C/Y
Note: Conservative investments are for short term (1-5 years); aggressive growth
investments are best for long term (6+ years).
Example 3. Calculate the monthly contribution needed to save up for a 5% down payment
in 8 years on a home worth $300 000. (Use the following, realistic, interest rates to set up
your calculations)
GIC: 3%
5 year bond: 4%
10 year bond: 6%
Equity return average: 10%
N
I
PV
PMT
FV
P/Y
C/Y
Budget (Based on growth income):
-
Recommended
Housing 35% (Rent, mortgage, utilities)
Food/Restaurants 10%
Savings 10% (TFSA, RRSP)
Transportation 10% (Car, gas, insurance, maintenance)
Debt 10% (Student Loans)
Donations/Charity 5%
Other 15%
Matty 2016
Actual?
Math 11
Unit 7 - Finances
Unit Notes Package
Example 4. Find the down payment and monthly investment needed over 8 years on a $300
000 home if:
-
Down payment minimum 5%, maximum 20%
Investment interest is conservative (1.5%) or non-conservative (4%)
A: 5% down
at 1.5%
interest
N
I
PV
PMT
FV
P/Y
C/Y
Matty 2016
B: 5% down
at 4%
interest
C: 20% down
at 1.5%
interest
D: 20% down
at 4%
interest
Math 11
Unit 7 - Finances
Unit Notes Package
Finance Project Unit
Lesson 5: Stress Test
Car Research – ASSIGNMENT!
- Use autotraders.ca or craigslist.ca AND bring a print out of 2 cars (new or used)
- Bank/Dealership qualifies you for 2xGross Income
- Bring the bank/dealerships lending rate on a car
o If you are having trouble finding the rate, print out a line of credit prime rate
and used prime plus 4%
Home Stress Test
Example 1. Calculate the monthly payments for a $350 000 mortgage at 3.2% compounded
annually with 25 year amortization.
N
I
PV
PMT
FV
P/Y
C/Y
Example 2. After 5 years, your mortgage now needs renewal.
a) How many payments do you have left after the 1st 5 years are up?
b) How much do you still owe after the 5 years if the mortgage rates decrease by 3% per
year?
c) Calculate the new mortgage payment if your loan rate increases by 2%.
N
I
PV
PMT
FV
P/Y
C/Y
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
Finance Project Unit
Lesson 6: Car Purchase Part I
Example 1. Find the depreciation rate after 5 years for:
a) A new $50 000 BMW sold at $20 000
N
I
PV
PMT
FV
P/Y
C/Y
b) A used $30 000 Acura sold at $14 000
N
I
PV
PMT
FV
P/Y
C/Y
Example 2. Calculate the total cost for buying a new truck $50 000 at 1% annually, financed
over 5 years.
a) Find payments/month (assume no down payment)
N
I
PV
PMT
FV
P/Y
C/Y
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
b) Find the financial charge
c) Find lost depreciation (at 17% annually)
d) Find true total charge (FC and depreciation)
Resources to research buying a car
http://www.consumerreports.org/cro/2012/12/how-to-spot-a-lemon/index.htm
Purchase a car – http://www.autotrader.ca/
New car price – https://carcostcanada.com/Home/
Used car price – http://www.vmrcanada.com/
Vehicle reliability – http://www.consumerreports.org/cro/index.htm (note: subscription
to site $6/mo)
Car history – https://www.carfax.com/ ;carproof.com (note: need a vin#. One time fee of
approx $25)
Mechanic Check – $130 use a local independent mechanic, not dealers.
Things to consider:
1. KM-average: 20 000 km/yr
2. Avoid small dealerships
3. Insurance: $150-$200/month. Gas: $100 - $200/month. Repairs: $50/month
4. Overall reference of vehicle reliability:
http://www.consumerreports.org/cro/cars/guide_to_car_reliability/index.htm
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
Finance Project Unit
Lesson 7: Car Purchase Part II
ROI: Return on investment (compounded annually)
Example 1. You buy a used 2010 Westwood Honda civic for $12 000, financed at 7% over 5
years. VMR shows a 2010 Civic for $10 500 and a 2005 Civic $6300. Consumer reports
show 3 full black marks. Calculate:
a) Depreciation rate, based on VMR comparisons.
b) Financial charge for the Westwood Honda Civic.
c) Future value of your Westwood Honda in 5 years (how much you can sell it for)
supposing the consumer report shows a 9.7% depreciation rate.
d) Your expected lost depreciation for the Westwood Honda (how much money you
lost)
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
Example 2. Adam and Bob are high school friends. They invest the same amount of money
in the same stock, but for different amounts of time as described below.
Adam
$50/month invest
Starts with $0
8% interest
Compounded monthly
10 years
Bob
$50/month investment
Starts with 0$
8% interest
Compounded monthly
40 years
a) Calculate how much they invested
b) Oddly, Adam ends up with more money at retirement. How is this possible?
Example 3. Compare the difference between a conservative ROI of 4% annually with a 10%
ROI over 40 years.
Person A
$200 monthly investment
4% interest
40 years
$10 000 deposit
A
N
I
PV
PMT
FV
P/Y
C/Y
Matty 2016
Person B
$200 monthly investment
10% interest
40 years
$10 000 deposit
B
Math 11
Unit 7 - Finances
Unit Notes Package
Finance Project Unit
Lesson 8: Opportunity Cost/Investments
Example 1. A new truck costs $50000 and is financed at 2% compounded annually over 5
years. Note: 60% of its value is lost. Using monthly installments, calculate the financial
charge and the actual cost of the car.
A
B
N
I
PV
PMT
FV
P/Y
C/Y
Total amount paid =
Financial charge = Total amount paid – Cost of the car
The car salesman is trying to convince you to buy the truck and tells you that the extra
charge in financing is only ______$ per day.
Lost Depreciation =
Actual cost of a car = Financial Charge + Lost Depreciation
Your talk to your accountant before the deal is final and together have calculated that this
truck will actually cost you ______$ per day.
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
Opportunity Cost: The value of an alternative investment you could have invested in
Suppose instead of bying the new truck in the above example, you went for a cheaper
option and invested the left over money. Given the following three scenarios, what is the
opportunity cost of scenario A? (remember, your original PMTs were $855)
A
B
C
$855
$855
$855
Very used car $155/m
Slightly used car $355/m
Bus $55/m
$700/m to invest
$500/m to invest
$800/m
NOTE: Use a 6% alternate investment to determine future value of the money being
invested.
A
N=
I=
PV =
PMT =
FV = ___
P/Y =
C/Y =
Your FOM 11 brain kicks in and before you finalize the deal for the truck, you drop the deal
because economically it costs you ___________$ per day.
Remember:
Used cars should have approximately 20000 km/year (check carfax to ensure no rollback).
An ideal car is approximately 4-6 year old car with low KM.
The majority of the depreciation will have been lost but the reliability of the car will be
good.
Matty 2016
Math 11
Unit 7 - Finances
Unit Notes Package
Example 2. What is the opportunity cost for a $5/day Starbucks habit? (30 days/m 6%
compounded annually, age 18 – 65)
N=
I=
PV =
PMT =
FV =
P/Y =
C/Y =
Matty 2016