BMTH 110 Test 3 Review
Round all monetary values to two decimal places.
1) Mr. Pitcher obtained a $40 000 loan for making over his house. The loan requires seven
equal annual payments at the end of each year at 11.7% p.a compounded semi-annually.
a. Compute the size of the annual payments.
b. Construct a partial amortization schedule displaying only the first two and last two
payments for the loan. Include the amount paid, interest paid, principal repaid, and
outstanding balance.
2) A car costs $22 500. Alternatively, the car can be leased for four years by making payments
of $380 at the beginning of each month and can be bought at the end of the lease for
$5200. If interest is 8.9% p.a. compounded semi-annually, should the car be purchased
or leased?
3) Mary bought a piano priced at $17 500 for 10% down and the balance in equal monthly
payments over four years at 9.5% p.a. compounded monthly.
a. How much does Mary have to pay at the end of each month?
b. What is the outstanding balance after three years?
c. What is the interest paid in the 37th payment?
d. What is the principal repaid in the 37th payment?
e. What is the total interest included in the payments?
4) An investor has two investment alternatives. If he chooses Alternative 1, he will have to
make an immediate outlay of $7000 and will receive $650 at the end of every three months
for the next eight years. If he chooses Alternative 2, he will have to make an immediate
outlay of $8000 and will receive $34 000 after eight years.
If interest is 11% p.a. compounded quarterly, which alternative should the investor choose
on the basis of the net present value criterion?
5) A $52 000 mortgage amortized by monthly payments over 25 years is renewable after five
years. Interest is 9.2% p.a. compounded semi-annually.
a. What is the size of the monthly payments?
b. Determine the balance at the end of the five-year term.
c. If the mortgage is renewed for a three-year term at 8.5% p.a. compounded semiannually, compute the size of the monthly payments for the renewal term.
6) A firm considering the purchase of a $10 000 machine that would reduce labour cost by
$4000 in each of Year 1 and Year 2, and by $3000 in each of Years 3 and 4. The machine’s
salvage value at the end of Year 4 is $1000. Should the machine be purchased at 12% p.a.
compounded annually?
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BMTH 110 Test 3 Review
Round all monetary values to two decimal places.
7) A debt of $42 000 is repaid by payments of $1850 at the end of every six months. Interest
is 7.3% p.a. compounded semi-annually.
a. How many payments are needed to repay the debt?
b. What is the size of the final payment?
8) Swim Company borrowed $50 000 for replacement of equipment. The debt is repaid in
payments of $2200 made at the end of every three months.
a. If interest is 7.2% p.a. compounded semi-annually, how many payments are needed to
pay off the debt?
b. What is the principal repaid during the first year?
c. How much interest is paid during the first year?
9) Mason Inc. has to consider two proposals. Alternative A offers net returns of $1600 at
the end of each year for 10 years. Alternative B offers net returns of $6000 each year after
four, seven, and 10 years respectively. Determine the preferred alternative according to
the discounted cash flow criterion if interest rate on the return is 14% p.a. compounded
annually.
10) A lease valued at $28 000 requires payments of $1200 every three months due in advance.
If the money is worth 6.8% p.a. compounded monthly, what is the size of the final lease
payment?
11) Rachel borrowed $7500 at 12.2% p.a. compounded quarterly to purchase new equipment.
Payments of $1600 are made at the end of every three months.
a. Calculate the number of payments to amortize (pay off) the loan.
b. Construct the full amortization schedule for the loan showing the total paid and the
total interest paid of the loan.
12) Replacing old equipment at an immediate cost of $58 000 and $60 000 six years from now
will result in a saving of $7600 semi-annually for 10 years. At 12.6% p.a. compounded
annually, should the old equipment be replaced?
13) A loan of $12 000 is repaid by payments of $765 at the end of every month. Interest is
9.9% p.a. compounded quarterly.
a. How many payments are required to repay the debt?
b. What is the size of the final payment?
14) A choice has to be made between two investment proposals. Proposal A requires an
immediate outlay of $55 000 and a further outlay of $40 000 after four years. Net
returns are $18 000 per year for 11 years. The investment has no residual value after 11
years.
Proposal B requires outlays of $35 000 in each of the first three years will yield returns
of $95 000 in year 4 and $90 000 in Year 5. The residual value of the investment after
11 years is $20 000.
Which proposal is preferable at 12% p.a. compounded annually?
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The Math Centre
Liberal Arts and Science
North Campus: GH203, Lakeshore: F201 & www.humber.ca/liberalarts/math-centre
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BMTH 110 Test 3 Review
Round all monetary values to two decimal places.
Answers/Solutions
1) a. $8776.45
b.
Payment
0
1
2
Initial Balance
Interest
Principal
Payment
$40 000
$36 040.44
$4 816.89
$4 340.07
$3 959.55
$4 436.38
$8 776.45
$8 776.45
Closing Balance
$40 000
$36 040.44
$31 604.07
6
7
$14 844.41
$7 833.16
$1 785.19
$943.29
$6 991.26
$7 833.16
$8 776.45
$8 776.42
$7 833.16
$0.00
2) Leased. $19 128.79
3) a. $395.69
b. $4 512.69
c. $35.73
d. $359.96
e. $3 243.12
4) Alternative 1. $6 715.21
5) a. $437.40
b. $48 515.35
c. $416.53
6) Yes. NPV = $1 437.62
7) (a) 50 payment
(b) $387.68
8) (a) 30 payments
(b) $5 373.51
(c) $3 426.49
9) Alternative A. $8 345.79
10) $449.95
11) a. 6 payments
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Liberal Arts and Science
North Campus: GH203, Lakeshore: F201 & www.humber.ca/liberalarts/math-centre
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BMTH 110 Test 3 Review
Round all monetary values to two decimal places.
b.
Payment
0
1
2
3
4
5
6
Payment ($)
Interest
$1 600.00
$1 600.00
$1 600.00
$1 600.00
$1 6000.00
$219.06
$228.75
$186.93
$143.83
$99.42
$53.65
$6.48
Principle
$7 500
$1371.25
$1 413.07
$1 456.17
$1 500.58
$1 546.35
$212.58
Balance
$6128.75
$4 715.68
$3 259.51
$1 758.93
$212.58
$0.00
12) No. NPV = $-1 062.53
13) a. 17 payments
b. $655.99
14) Proposal A. NPV = $26 457.86
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