# Calculating Mortgage Payments in Canada

Document Sample

```					Chapter 9 Personal Finance
9.1

MATHPOWERTM 11, WESTERN EDITION   9.1.1
Types of Income
Gross Income is the amount of money
earned through employment.
Employers offer earning in different ways:
• Salary: This is a fixed amount of money earned over
a specified time period, such as monthly or yearly.
• Wage: This is money earned hourly, daily, or by
piecework. Overtime and gratuities may also be
included in a person’s wage.
• Commission: This is earnings based on a percent of
an employee’s sales during the pay period and may
be paid in combination with a salary or wage.
• Graduated Commission: This is earnings based on
commission, in which the rate of commission increases
when sales reach a certain goal.                    9.1.2
Calculating Gross Earnings
Sandra works full time at a retail clothing store. She is
paid \$8.75/h plus time-and-a-half for overtime, which
is any time over 40 h per week. One week she worked
48.5 hours. Calculate her gross earnings for the week.
Regular Earnings:      Hours worked x Hourly wage
40 x \$8.75 = \$350
Overtime Earnings: Hours worked x Hourly wage x 1.5
8.5 x \$8.75 x 1.5 = \$111.56

Total Earnings:        Regular + Overtime Earnings
\$350 + \$111.56 = \$461.56
Sandra’s gross earnings for the week were \$461.56.
9.1.3
Calculating Gross Earnings
Paul, Stan, and Jody work for the same company but are
paid in different ways. Paul is paid a straight commission
of 6% of his total sales. Stan is paid a base salary of
\$475 per week plus 3.5% of sales above a sales quota of
\$5000. Jody is paid a graduated commission of 2.5% on
sales up to \$3000, plus 6.5% on sales in excess of \$3000.
If each persons sales for one week were \$16000, calculate
the gross income for each.
Paul:    6% of \$16 000 = 0.06 x \$16 000 = \$960
Stan:    \$475 + 3.5% of \$11 000 = \$860

Jody:    2.5% of \$3 000 + 6.5% of \$13 000 = \$920
9.1.4
Calculating Overtime Rate of Pay
Henry earns \$10.50/h plus extra for overtime. His normal
work week is 40 h. Last week he worked 51 h and his gross
earnings were \$598.75. What is his overtime rate of pay?

Regular Earnings:     40 x \$10.50 = \$420

\$598.75 - \$420 = \$178.75
Henry earned \$178.75 in overtime wages. He did this
with working 11 h in overtime.

Overtime: 11x = \$178.75           Henry’s overtime
x = \$178.75 ÷ 11      rate of pay is \$16.25.
x =\$16.25
9.1.5
Suggested Questions:
Page 530 and 531
1, 5, 7-10,
12, 16, 19, 21,
24, 25                 9.1.6
Chapter 9 Personal Finance
9.2

MATHPOWERTM 11, WESTERN EDITION   9.2.1
Net Income
After all deductions are subtracted from the gross
income, the amount that the employee actually receives
is called the net income.
There are certain deductions which an employer must
make from the employees paycheque:
Employment Insurance (EI)
Income Tax, both federal and provincial
Other possible payroll deductions include: union dues,
professional dues, life insurance premiums, parking
fees, registered pension plan contributions (RPP)
Taxable Income is gross income subtract any tax-exempt
deductions: union or professional dues, RPP, RRSP
9.2.2
Net Income [cont’d]
Canada Pension Plan is money that the government collects
toward an employee’s future pension. One year the CPP
contributions were 3.2% of the gross income. The first
\$3500 is the basic CPP exemption and is not subject to
CPP contributions.
Employment Insurance is an insurance plan where, if an
employee has paid the minimum number of premiums,
then the plan provides some income during periods of
unemployment. One year the EI premiums were 2.7%
of gross income, up to a maximum of \$1053.

9.2.3
Calculating EI and CPP Contributions
Angie is paid biweekly and has gross earnings of
\$1160. Calculate her CPP contributions and her
Gross Annual Income:      26 x \$1160 = \$30 160
CPP Contributions:     Gross Income - Basic Exemption
\$30 160 - \$3500 = \$26 660
3.2% of \$26 660 = \$853.12
Biweekly CPP Contributions:      \$853.12 ÷ 26 = \$32.81
EI Contributions:             2.7% of \$30 160 = \$814.32
Biweekly EI Contributions:       \$814.32 ÷ 26 = \$31.32
Angie’s biweekly CPP contribution is \$32.81 and her
EI contribution is \$31.32.                            9.2.4
Calculating Federal and Provincial Tax
Income Tax: The amount of income tax deducted
depends upon the employee’s income and tax credits.
Basic Personal Tax Credits are deductions granted for
each person that the employee supports.

Alberta Provincial Tax Rate: 45.5% of basic federal tax
9.2.5
Calculating Net Annual Income
Alina earns \$1020 per week. Each week she pays \$85
into an RRSP, \$6.50 for union dues, and \$7 for medical
insurance. Her basic tax credit is \$6456.
a) Calculate annual deductions for CPP and EI.
b) Find the total amount of income tax deducted.
c) Determine her net annual income.

a) CPP Contributions:       52 x \$1020 = \$53 040
\$53 040 - \$3500 = \$49 540
\$49 540 x 0.032 = \$1585.28

EI Contributions:    0.027 x \$53 040 = \$1432.08

9.2.6
Calculating Net Annual Income [cont’d]
b) Federal Income Tax: Calculate taxable income first.
Taxable Income = gross income - tax-exempt deductions
= \$53 040 - 52(\$85 + \$6.50)
= \$48 282
Federal Tax (using the table):
= 17% of \$29 590 + 26% of (\$48 282 - \$29 590)
= 0.17 x \$29 590 + 0.26 x \$18 692
= \$9890.22
Tax Credits = Basic Personal Tax Credit + CPP + EI
= \$6456 + \$1585.28 + \$1432.08
= \$9473.36
Basic Federal Tax = Federal Tax - 17% of tax credits
= \$9890.92 - 0.17 x \$9473.36
= \$8279.75                        9.2.7
Calculating Net Annual Income [cont’d]
Provincial Tax: = 45.5% of Basic Federal Tax
= 0.455 x \$8279.75
= \$3767.29
Total income tax deducted = \$8279.75 + \$3767.29
= \$12 047.04
c) Total Deductions
= CPP + EI + income tax + tax-exempt deductions
+ any other deductions
= \$1585.28 + \$1432.08 + \$12 047.04 + 52(\$85 + \$6.50 + \$7)
= \$20 186.40
Net Annual Income = Gross Income - Total Deductions
= \$53 040 - \$20 186.40
= \$32 853.60                         9.2.8
Suggested Questions:
Pages 536 and 537
1-4,
5-25 odd,
30, 33            9.2.9
Chapter 9 Personal Finance
9.3

MATHPOWERTM 11, WESTERN EDITION   9.3.1
Simple Interest
Interest is the rent paid for the use of someone else’s
money. The rate at which this interest is paid is
expressed as a percentage of the amount of money
loaned per unit of time. This amount of money
loaned is called the principal.

Interest = Principal x Rate x Time
The total sum of money repaid, principal plus interest
is called the amount.

Amount = Principal + Interest

9.3.2
Calculating Simple Interest
A boat motor costs \$2500. Mr. Wilson pays \$1700
down and the balance at the end of 4 months with a
service charge of 24% per annum simple interest.
What amount must he pay at the end of the 4 months?
Amount financed:           \$2500 - \$1700 = \$800

Simple Interest:           I = PRT
4
I=?                        I = 800 x 0.24 x
12
P = \$800
R = 24%
= 64

T=
4           Mr. Wilson will pay \$64 in simple
12          interest, making his payment
amount \$864.00
9.3.3
Compound Interest
Compound interest is when an amount of money,
P (principal), is invested at an interest rate, i,
compounded annually. The accumulated amount, A,
is given by the formula, A = P(1 + i)n.
Calculating Compound Interest
Determine the accumulated amount of \$6800 invested
at 6.75%/a compounded annually for 15 years.
A=?           A = P(1 + i)n
P = \$6800       = 6800(1 + .0675)15
i = 6.75%      = 18 114.53
n = 15
The accumulated amount is \$18 114.53.
9.3.4
Calculating Compound Interest
Note that there are two variables that will be affected by
how the interest is compounded - the i (the interest rate)
and the n (the number of compounding periods).
Interest is given to you as a yearly amount. for example,
12% per annum. So, when you are compounding it
semiannually, you are dividing this amount into two parts:
6% for the first part and 6% for the second.
Interest           For interest (i)     For # of periods (n)
Annual             Divide by 1          Multiply by 1
Semi-annual        Divide by 2          Multiply by 2
Quarterly          Divide by 4          Multiply by 4
Monthly            Divide by 12         Multiply by 12
Daily              Divide by 365        Multiply by 365
9.3.5
Calculating Compound Interest
Paul invested \$12 000 in an account with an interest rate
of 11%/a compounded semi-annually. How much will
he be able to withdraw in 5 years?
A=?
P = \$12 000                        A = P(1 + i)n
i = 11%     Since there are 2        = 12000(1 + 0.055)10
interest periods
2                               = 20 497.73
per year.
n = 10    Since there are
5 x 2 = 10 periods
in 5 years.          Paul could withdraw
\$20 497.73 in 5 years.

9.3.6
Comparing Compound and Simple Interest
You have \$5000 you wish to deposit. Bank A pays 12%
simple interest per annum. Bank B pays 10% compounded
quarterly. If you plan to invest your money for 10 years,
which bank would give you the best return? Calculate the
difference in the amount of interest paid.
Bank A                          Bank B
I = PRT                         A = P(1 + i)n
= 5000 x 0.12 x 10              = 5000(1 + 0.025)40
= \$6000                         = \$13 425.32
A=P+I                           I=A-P
= 5000 + 6000                   = 13 425.32 - 5000
= \$11 000                       = \$8425.32
Bank B will pay the greater amount of interest by
\$8425.32 - \$6000 = \$2425.32.                        9.3.7
Comparing Banking Options
A bank offers an interest rate of 8% per year compounded annually.
A second bank offers an interest rate of 8% per year, compounded
quarterly. If \$2000 were deposited for 10 years in each bank,
which bank would give the better return and by how much?

Bank A                                 Bank B

A = P(1 + i)n                          A = P(1 + i)n
= 2000(1 + 0.08)10                     = 2000(1 + 0.02)40
= \$4317.85                             = \$4416.08

Bank B would have the better return by
\$4416.08 - \$4317 .85 = \$98.23.
9.3.8
A loan of \$5000 carries an interest rate of 9% per year, compounded
monthly. Adele makes payments of \$350 per month. Determine how
much she still owes after making 12 payments.
Bala nce        Inte re st       Payme nt        Ne w Balance

\$   5,00 0.00    \$     37 .5 0   \$   35 0.00    \$       4,68 7.50
\$   4,68 7.50    \$     35 .1 6   \$   35 0.00    \$       4,37 2.66
\$   4,37 2.66    \$     32 .7 9   \$   35 0.00    \$       4,05 5.45
\$   4,05 5.45    \$     30 .4 2   \$   35 0.00    \$       3,73 5.87
\$   3,73 5.87    \$     28 .0 2   \$   35 0.00    \$       3,41 3.89
\$   3,41 3.89    \$     25 .6 0   \$   35 0.00    \$       3,08 9.49
\$   3,08 9.49    \$     23 .1 7   \$   35 0.00    \$       2,76 2.66
\$   2,76 2.66    \$     20 .7 2   \$   35 0.00    \$       2,43 3.38
\$   2,43 3.38    \$     18 .2 5   \$   35 0.00    \$       2,10 1.63
\$   2,10 1.63    \$     15 .7 6   \$   35 0.00    \$       1,76 7.39
\$   1,76 7.39    \$     13 .2 6   \$   35 0.00    \$       1,43 0.65
\$   1,43 0.65    \$     10 .7 3   \$   35 0.00    \$       1,09 1.38
9.3.9
Annuities
An annuity is an investment plan in which fixed
amounts of money are deposited or paid out at
regular intervals over a specified period of time.
Paul invests \$1000 every 6 months, beginning in Oct., at 6%/a
compounded semi-annually. How much will he have at the end of 2 a?

1000                                                1000(1 + 0.03)4
1000                                      1000(1 + 0.03)3
1000                         1000(1 + 0.03)2
1000           1000(1 + 0.03)1
= 1000(1 + 0.03)4 + 1000(1 + 0.03)3 + 1000(1 + 0.03)2 + 1000(1 +0 .03)1
= 1125.51 + 1092.73 + 1060.90 + 1030.00
= \$4309.14                                                       9.3.10
6-month
Principal     Interest       Amount
period
1      1000         30             1030
2      2030         60.9           2090.9
3      3090.9       92.727         3183.627
4      4183.627     125.5088       4309.136

1              1000            =B1*0.03         =B1+C1
2              =D1+B1          =B2*0.03         =B2+C2
3              =D2+B1          =B3*0.03         =B3+C3
4              =D3+B1          =B4*0.03         =B4+C4

9.3.11
Suggested Questions:
Pages 542 and 543
1-4
5-29 odd,
34, 36, 37       9.3.12
Chapter 9 Personal Finance
9.4

MATHPOWERTM 11, WESTERN EDITION   9.4.1
The Effective Annual Rate
The Nominal Interest Rate is the stated or named rate of
interest of an investment or a loan. This is usually a
compounded rate.
The Effective Annual Rate is the simple interest rate
that would produce the same interest as the nominal
interest rate.
An investment pays interest at 8% compounded
semi-annually. What is the effective annual interest rate?
Find the accumulated amount of \$1 in one year:
Therefore the
A = P(1 + i)n      Find the amount of
Effective Annual
A = 1(1 + 0.04)2   interest:
Rate of interest is
A = 1.0816         1.0816 - 1 = 0.0816
8.16%.
9.4.2
Applying The Effective Annual Rate
You can use the effective annual interest rate to decide
which interest option might be better.
Option A: 8.30% compounded quarterly
Option B: 8.35% compounded semi-annually
Option A                                Option B

Interest = 8.30 ÷ 4                     Interest = 8.35 ÷ 2
= 2.075%                                = 4.175%

A = P(1 + i)n                            A = P(1 + i)n
= 1(1 + .02075)4                        = 1(1 + 0.04175)2
= 1.0856                                 = 1.0852
Therefore, the effective                 Therefore, the effective
annual rate of interest                  annual rate of interest
is 1.0856 - 1 = 0.0856                   is 1.0852 - 1 = 0.0852
= 8.56%.                                 = 8.52%.
9.4.3
Suggested Questions:
Page 549
1-3,
4-15 even         9.4.4
Chapter 9 Personal Finance
9.5

MATHPOWERTM 11, WESTERN EDITION   9.5.1
Calculating the Cost of Financing
The Jamisons bought a colour television set. The price, including
tax, was \$736.70. They signed an installment contract agreeing
to pay 15% of the price as a down payment. The remainder,
plus finance charge, will be paid in 18 monthly installments of
\$41.16 each. What did the Jamisons pay for the TV? What is
the amount of the finance charge on the Jamisons’ account?
Calculate the down payment:            \$736.70 x 0.15 = \$110.51
Calculate the amount financed:     \$736.70 - \$110.51 = \$626.19
Calculate the amount paid:                18 x \$41.16 = \$740.88
Calculate the finance charge:       \$740.88 -\$626.19 = \$114.69
Total cost for the TV:            \$110.51 + \$740.88 = \$851.39

The Jamisons paid \$851.39 for the television set and the finance
charge was \$114.69.
9.5.2
Calculating the Finance Charges on Credit Cards
Having a charge card allows you to purchase your items at the
store and pay at a later date. Each month you receive a statement,
with a specified due date. The store computes the finance charge
on the balance that remains after payments have been subtracted
from the unpaid balance.
The example shows the summary of a customer’s account for
6 months. Monthly credit charges are 1.5%
Prev ious   Pa yment   Purchase    Ba lance   Credit       Ne w
Month      Ba lance     Made     Charged       Due      Charge     Ba lance
Ja nua ry   \$5 62.80     \$3 00     \$1 97.28   \$4 60.08    \$6 .9 0   \$4 66.98
Fe bruary   \$4 66.98     \$2 00      \$5 6.90   \$3 23.88    \$4 .8 6   \$3 28.74
March     \$3 28.74     \$1 50     \$2 73.26   \$4 52.00    \$6 .7 8   \$4 58.78
April     \$4 58.78     \$2 50     \$1 03.85   \$3 12.63    \$4 .6 9   \$3 17.32
May     \$3 17.32     \$2 00      \$2 4.95   \$1 42.27    \$2 .1 3   \$1 44.40
June     \$1 44.40     \$1 00      \$9 8.00   \$1 42.40    \$2 .1 4   \$1 44.54

For the 6 month period, the interest charged was \$27.50.
9.5.3
Credit Card Statements              7   6
Card         Previous       This
Number       Statement      Statement           Payment Due
12345678     Sept. 18       Oct. 18             Nov. 10

Posting
Date         Description                        Amount
25-Sep       Super Store                        \$    72.50
10-Oct       Payment                            \$   120.00
15-Oct       Zellers                            \$   126.99

Previous
Balance
\$ 263.82
Tom received the above credit card statement. The interest charge
is 0.0504% daily. The minimum payment is 5% of the new balance.
9.5.4
Credit Card Statements [cont’d]
a) Calculate the interest charges. b) Calculate the total purchases.
c) Calculate the new balance. d) Calculate the minimum payment.
e) If Tom pays \$200 on Nov. 10 and decides to pay the balance on
Nov. 15, how much will his final payment be?
a) Calculate the interest charges:
On the previous balance:           On purchases on Sept. 25:
I = PRT                            I = PRT
= \$263.82 x 0.000504 x 30         = \$72.50 x 0.000504 x 23
= \$3.99                           = \$0.84
On purchases on Oct. 15:
I = PRT
= \$126.99 x 0.000504 x 3
= \$0.19
Total interest = \$3.99 + \$0.84 + \$0.19
= \$5.02
9.5.5
Credit Card Statements [cont’d]
b) Calculate the total purchases:
Purchases = \$72.50 + \$126.99
= \$199.49

c) Calculate the new balance:
New Balance = \$ 263.82 + \$5.02 + \$199.49 - \$120.00
= \$348.33

d) Calculate the minimum payment:
Minimum payment = 5% of balance
= 0.05 x \$348.33
= \$17.42

4   9.5.6
Credit Card Statements [cont’d]
e) If Tom pays \$200 on Nov 10 and decides to pay the
balance on Nov. 15, how much will his final payment be?

From Oct. 18 to Nov. 10, not including Nov. 10, is 22 days.
I = PRT                       Balance = \$348.33 + \$3.86 - \$200
= \$348.33 x 0.000504 x 22            = \$152.19
= \$3.86
From Nov. 10 to Nov. 15, not including Nov. 15, is 5 days.
I = PRT
= \$152.19 x 0.000504 x 5
= \$0.38

Final Payment = \$152.19 + \$0.38
= \$152.57
4    9.5.7
Suggested Questions:
Pages 555 and 556
1, 2, 7, 11,
16, 21, 28, 29
9.5.8
Chapter 9 Personal Finance
9.6

MATHPOWERTM 11, WESTERN EDITION   9.6.1
Mortgages
A mortgage is a legal contract, registered at the land
registry office which is operated by the provincial
government. In a mortgage contract, the purchaser
agrees to repay the loan according to the terms of the
mortgage and offers the house as security.
The term of the mortgage is the length of time for which
The amortization period is the length of time that it
would take for the loan to be paid in full.

9.6.2
Calculating Monthly Mortgage Payments
Tom bought a house for \$215 000. He paid down 25%
and arranged a 5-year mortgage at 6.75% per annum,
amortized over 25 years. Find his monthly payments.
Find the amount of the mortgage:
25% of \$215 000 = \$53 750
\$215 000 - \$53 750 = \$161 250
From the chart (see page 590 or the next slide),
the monthly payment for each \$1000 of mortgage
debt amortized over 25 years is \$6.85.
\$161 250 = 161.25 x 1000
Monthly payment = 161.25 x \$6.85
= \$1104.56
9.6.3
9.6.4
Calculating Property Tax
Property Tax:    The rate at which property tax is
calculated is called the mill rate. The
mill rate is the amount of tax levied
annually for each \$1000 of assessed
value of the property.

assessed value
Annual Property Tax
=             mill rate
1000
The assessed value of a house is \$184 000. The
mill rate is 21.785. Find the property tax.
184 000
Pr operty Tax=           21.785
1000
= \$4008.44
9.6.5
Suggested Questions:
Pages 560 and 561
1, 5, 11, 14,
23, 26, 30, 38         9.6.6
Chapter 9 Personal Finance
9.7

MATHPOWERTM 11, WESTERN EDITION   9.7.1
Balancing a Budget
A balanced budget is one for which the total expenditure equals
the total income.
Fixed expenses occur regularly. Some examples of fixed expenses
are things like mortgage and car payments.
Variable expenses can also be regular but are more easily
controlled. Some examples would include things like the food,
transportation, and entertainment.
Occasional expenses occur once or twice in a year or unexpectedly.
Some examples are the family vacation and home renovations.

9.7.2
Calculating Expenses
If the club had a total of
\$2400, calculate the amount
spent for each expense.

Ice Rental    \$720

Uniforms      \$ 600

Travel        \$ 480

Equipment     \$ 360

Misc          \$ 240

\$2400     9.7.3
Balancing a Budget
One year Paul’s net income was \$31 340 and he received \$2850
from an investment. His total annual expenses were
Rent          \$9600          Utilities         \$840
Food          \$5420          Telephone         \$342
Cable TV        \$284         Home Insurance     \$285
Car Licence     \$110         Car Insurance     \$1125
Car Repairs   \$1720          Gasoline          \$1840
Clothing       \$2170         Entertainment     \$3450
Material       \$185          Products           \$395
Donations       \$625         Miscellaneous     \$1265
Complete an annual budget statement for Paul.                    6
Was it a balanced budget?
What percent of his net income was Paul able to save?
9.7.4
Paul's Annual Budget Statement
Income

Ne t e mployme nt income     \$31 340
Inv es tme nts             \$ 2 850
Othe r

Total                             \$34 190

9.7.5
Paul’s Annual Budget Statement
Fixe d Expe nse s                    Variable Expe nse s                 Occasional Expe nse s

Rent                 \$    9,600.00   Food                \$    5,420.00   Home Repairs
Utilities            \$      840.00   Clothing            \$    2,170.00   Home Improv ements
Car Licence          \$      110.00   Gasoline            \$    1,840.00   Donations            \$     625.00
Car Insurance        \$    1,125.00   Entertainment       \$    3,450.00   Gifts                \$     685.00
Home Insurance       \$      285.00   Education/Reading   \$      185.00   Trav el              \$   1,725.00
Cable TV             \$      284.00   Personal Care       \$      395.00   Personal Business
Telephone           \$      342.00   Car Repairs          \$   1,720.00
Other                               Other                \$   1,265.00

Total                \$   12,244.00   Total               \$   13,802.00   Total                \$   6,020.00

Total Expenditures
\$      32,066.00

Balance
\$34 190 - \$32 066 = \$2 024

Since total income and total expenditures are not the same,
this is not balanced budget.                                                                           4
Therefore, he
Percent saved:    2024
 0.059       saved 5.9%.
34190                                                                            9.7.6
Suggested Questions:
Pages 565 and 566
1-18, 20, 21ab, 25ab
Chapter Review
Pages 572 and 573
1-28, 29a              9.7.7

```
DOCUMENT INFO
Shared By:
Categories:
Stats:
 views: 21 posted: 12/1/2010 language: English pages: 52
Description: Calculating Mortgage Payments in Canada document sample