Math Compilation

Question 1

Richard owns a 2,400 square foot unit in a strata complex. There are 19 other units, the square footage of which totals 37,600 square feet. The common property has an area of 12,600 square feet. The total common expenses for the year amount to $48,000. What is Richard’s monthly share of the common expenses?

(1) $596.83
(2) $255.32
(3) $761.90
(4) $240.00

Answer 1

4

2400 (unit entitlement) divided by total 40,000 (total unit entitlement) X 48,000 (total contribution)
= 2,880 divided by 12 (monthly) = 240

Option (4) is correct and Options (1), (2), and (3) are incorrect because a strata lot’s contribution to an expense is calculated as the unit entitlement of the strata lot divided by the total unit entitlement of all strata lots multiplied by the total contribution. Richard’s unit entitlement is 2,400, the total unit entitlement of all strata lots is 40,000, and the total contribution is $48,000. Richard’s annual share of the common expense is $2,880, and therefore his monthly share is $240.

Question 2

An investment corporation purchased an apartment building on March 31, 2003 for $2,800,000. Of that
$2,800,000, $1,700,000 was attributed to the building and $1,100,000 to the land. Depreciation was to be claimed at $50,000 per year for the life of the building. The building component of the property was valued on March 31, 2013, to be $2,400,000. What would be the net amount of the building appearing on the corporation’s Statement of Assets and Liabilities as at March 31, 2013?

(1) $1,700,000
(2) $1,200,000
(3) $2,400,000
(4) $1,900,000

Answer 2

2

appears to be 1700000 atributed to the building
minus
500000 depreciation ( 50,000 per year X 10)

=1,200,000

Question 3

Consider an asset with a purchase price of $185,000, economic life of 9 years, and $5,000 salvage value.
If you purchase the asset today, what will be its book value in three years?

(1) $125,000
(2) $150,000
(3) $175,000
(4) $190,000

Answer 3

1

180,000 divided by 9 years = 20,000 per year
6 years left = 120,000 + 5,000 salvage value

=$125,000

Question 4

An investor has decided to establish a bank account in order to accumulate sufficient capital at the end of seven years to purchase a boat. If the account pays interest at 3% per annum, compounded annually and the investor makes deposits of $8,000 at the end of each year, how much capital will he have accumulated at the end of seven years?

(1) $42,851.59
(2) $79,747.81
(3) $57,987.33
(4) $61,299.70

Answer 4

4

j1=3%
n=7

0 -8000 ?

=61,299.69

Question 5

A holding property was purchased ten years ago for $23,000. How much must it sell for now if the owner is to realize a pre-tax yield of j2 = 14%?

(1) $85,266.09
(2) $89,002.74
(3) $92,516.82
(4) $83,144.22

Answer 5

2

j2 = 14%
n= 10

-23,000 0 ?

=89,002.74

Question 6

An investor plans to pay $200,000 for a vacant lot which he feels will sell at the end of three years for
$280,985.60. What is the monthly interest rate the investor will earn? (Ignore real property taxes)

(1) 0.948879%
(2) 1.404928%
(3) 12%
(4) 2.873734%

Answer 6

1

Question 7

Kevin wants to purchase an investment which will give him payments of $450 at the end of every quarter for the next four years. If Kevin wants to earn an interest rate of 6% per annum, compounded quarterly, how much should he pay today for this investment?

(1) $8,069.57
(2) $7,224.92
(3) $6,359.07
(4) $6,983.29

Answer 7

3

j4 = 6%
n=16

? 450 0

=-6359.06

Question 8

What rate of interest per compounding period would allow savers to “double their money” in 8 compounding periods? Assume that you invest $100 today so that it will grow to $200 in eight compounding periods.

(1) 12.5%
(2) 10.609279%
(3) 25%
(4) 9.050773%

Answer 8

4

j1 = ? 
n= 8

-100 0 200

=9.051

Question 9

An investor has decided to establish a bank account in order to accumulate sufficient capital at the end of four years to purchase a boat. If the account pays interest at 2.5% per annum, compounded annually and the investor makes deposits of $6,000 at the end of each year, how much capital will she have accumulated at the end of four years?

(1) $24,915.09
(2) $26,491.51
(3) $28,018.91
(4) $25,357.92

Answer 9

1

j1=2.5
n=4

0 -6000 ?

=$24,915.09

Question 10

A holding property was purchased 10 years ago for $23,000. How much must it sell for now if the owner is to realize a pre-tax yield of j2 = 6%?

(1) $30,910.08
(2) $41,540.56
(3) $45,189.50
(4) $38,246.54

Answer 10

2

j2=6%
n=10

-23,000 0 ?

=$41,540.55

Question 11

Johnny F. Lane wants to purchase a sports car which will be introduced to the market 10 months from now for $19,800. How much money should Johnny deposit in the bank today if he can earn 9% per annum, compounded monthly in his savings account?

(1) $18,374.46
(2) $7,856.84
(3) $19,800.00
(4) $18,018.00

Answer 11

1

j12=9%
n=10

? 0 19,800

=-18,374.46

Question 12

An investor wants to decide whether to buy a mortgage which calls for monthly payments of $390 for 20 years. If the investor can earn j2 = 8% in other investments, at what price should the mortgage be purchased?

(1) $48,921.57
(2) $46,626.12
(3) $45,232.84
(4) $47,081.12

Answer 12

4

2    2nd  pmt 
8  i/yr
2nd    eff%
12   pmt
2nd i/yr
=7.87  
240 N 
-390 PMT 
= 226,037.44

then you are going to start from the very beginning again, and plug in the FV instead of the PMT to get the PV

2    2nd  pmt 
8  i/yr
2nd    eff%
12   pmt
2nd i/yr
=7.87  
240 N 
FV = 226,037.44 
PV = 47,081.12

Question 13

A constant payment mortgage is written for $48,951.77 and specifies payments of $548.91 per month for 15 years. The interest rate on this mortgage is approximately:

(1) 12% per annum, compounded semi-annually.
(2) 8% per annum, compounded semi-annually.
(3) 10% per annum, compounded semi-annually.
(4) 11% per annum, compounded semi-annually.

Answer 13

4

j12=?
n=15(180)

48,951.77 -548.91 0

j12 conver to j2 = 11%

Question 14

A constant payment mortgage is written for $48,951.77 and specifies payments of $520 per month for 15 years. The interest rate on this mortgage is:

(1) j2 = 10.257982%
(2) j4 = 11.963722%
(3) j12 = 9.797818%
(4) all of the above

Answer 14

3

j12
n=15X12(180)

48,951.77 -520 0

j12=9.79

Question 15

Mr. Johnston’s house in Burnville, BC has been assessed at $110,000 for property tax purposes. The following tax rates have been set by the municipality and other taxing authorities:

General Tax Rate 5.13
School Tax Rate 4.24
Hospital District Tax Rate 0.137

What will be Mr. Johnston’s gross taxes payable on this property?

(1) $1,045.77
(2) $564.30
(3) $950.70
(4) Not enough information is given to determine the gross taxes payable

Answer 15

1

110,000/1000
=110

5. 13+4.24+.137=9.507000
6. 507000X110 = 1,045.77

Question 16

The total assessed value of all properties in the municipality of Grand River, BC is $2,900,765,800. The municipality needs to raise $13,623,500 through its general tax on real properties to finance its anticipated expenditures this year. All classes of property will be taxed at the same rate. Other taxing authorities have set the following tax rates for taxes to be collected by the municipality of Grand River:

School 6.1340
Hospital 0.3728
Regional District 0.0912

Hans Sum purchased his first home in Grand River last year; its assessed value is $123,729. Presuming that no taxes other than the above-mentioned taxes are collected, what will be Hans’ gross taxes payable on this property?

(1) $1,397.46
(2) $816.36
(3) $1,523.72
(4) $581.10

Answer 16

1

6.1340 + .3728 + .0912 = 6.598000

(123729/1000)123.729000X 6.598000=816.36

13623500/2900765800=.004697

.004697X123729=581.095527

581.095527 + 816.363942=1,397.459469

Question 17

A property recently sold for $378,500. The stabilized net operating income for the property was estimated to be $75,700 per annum. The estimated yield to the buyer is:

(1) 20%
(2) 11%
(3) 5%
(4) There is insufficient information to calculate an estimated yield.

Answer 17

1

75,700/378,500
=20%

Question 18

Blackacre, a revenue producing property, has been sold. The date of adjustment will be January 31, 1991, exactly 18 months after the contract of purchase and sale was signed and a deposit of $3,500 was paid directly to the seller. If interest on this deposit accrues for the benefit of the buyer, 6% per annum, compounded annually, what will be the amount shown on the seller’s statement of adjustment?

(1) $3,815.00 debit
(2) $3,819.68 debit
(3) $3,815.00 credit
(4) $3,819.68 credit

Answer 18

2

j1=6%
n=18

3500 0 ?

=3,819.60 debit to seller