MATH1091_Assignment_5
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MATH 1091: Business Mathematics
1
Student’s Name:
Calculator make and model:
Assignment 5
Total marks: 100
1.
A loan of $7,520 is to be repaid over 7 years with monthly payments and an interest rate of 19.0827%, compounded annually. Set up an amortization schedule
for the first two payments and the last two payments. (6 marks)
Payment
Period
Regular
Payment
Payment to
Interest
Payment to
Principal
Outstanding
Balance
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Assignment 5
2.
Greg and Terri purchased a $500,000 home with a $15,000 down payment. The balance is made up of a first mortgage of $90,000, which was amortized over 20 years with monthly payments. If the mortgage had an interest rate of 11%, compounded semi annually, provide the requested details below. (9 marks)
a)
The monthly payments
b)
The amount outstanding after the 24th payment
c)
A partial amortization schedule to show the first two payments and the last two payments of the loan
(a)
(b)
(c)
Payment
Period
Regular
Payment
Payment to
Interest
Payment to
Principal
Outstanding
Balance
3.
Harold signed a note for $5,000 and agreed to repay the note by one payment in 15 months. He also agreed to pay interest on the note every 3 months at the rate of 10.125%, compounded semi-annually. If Harold uses a sinking fund paying 18%, compounded quarterly, to accumulate the money to repay the face value of TRU Open Learning
MATH 1091: Business Mathematics
3
the note, answer the following questions. Assume the payments to the sinking fund are quarterly. (6 marks)
(a) Find the total cost of the debt to Harold.
(b) Construct a sinking fund schedule for the debt.
(a)
(b)
Year
Regular
Payment
Payment of
Interest
Increase in
Fund
Accum.
Balance in
Fund
Accum.
Book Value
of the Debt
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Assignment 5
4.
A local recreation commission is considering building a new arena that is expected to cost $1.5 million. The members of the commission need to decide if they should borrow the money and levy a tax on the local property owners to pay for the repayment of the debt. The cost of borrowing the money is 12%, compounded semi-annually, with the interest being payable every 6 months. The
money would be borrowed through the province and would require full payment in 5 years. If the commission decides to go ahead with the project, there will be a need to set up a sinking fund to handle the repayment of the debt. The sinking fund pays 10.25%, compounded annually. A friend of yours is a member of the commission and is complaining that he can’t
get the actual cost per year and the overall cost of the arena from the administration. Help him out by constructing the appropriate sinking fund schedule. Compute the annual and total cost of this project to the local taxpayers.
Note that total cost means the borrowing cost and sinking fund expenditures for the arena over the 5-year period. (6 marks)
Year
Regular
Payment
Payment of
Interest
Increase in
Fund
Accum.
Balance in
Fund
Accum.
Book Value
of the Debt
5.
A company wishes to set up a fund to replace a roof that will cost $170,000 5 years from now, making equal-sized payments at the beginning of each of the next 5 TRU Open Learning
MATH 1091: Business Mathematics
5
years. If money is worth 5% annually, what is the size of the annual payment? (3 marks)
6.
Calculate the interest and increase into the fund described in Problem 5 during the fourth payment period. (3 marks)
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Assignment 5
7.
Construct a partial sinking fund schedule to show the last two payments of the fund detailed below. (5 marks)
Amount to be created over 10 years: $80,000
Interest compounded semi-annually at 13%
Deposits made at the end of every 6 months
Year
Regular
Payment
Payment of
Interest
Increase in
Fund
Accum. Balance
in Fund
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MATH 1091: Business Mathematics
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8.
Determine the capital value (i.e., purchase price) of an investment in mining that is expected to provide a net annual income of $133,000 for 13 years and the have no income or residual value. This investment is expected to yield 14% compounded annually, and a depletion reserve earning 10.5% annually can be set up. (6 marks)
9.
If the mine described in Problem 8 could be sold for $6,000 when it was exhausted, what would be the capital value of the mine then? (6 marks)
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Assignment 5
10. How much should be paid for land containing an oil well that is estimated to produce for 10 years and have an annual income of $100,000? The prospective buyers wish to earn 15% on their investment, and they can set up a depletion reserve earning 7%. (6 marks)
11. Compute the yield rate on an investment in an orchard advertised for sale at $300,000. The orchard is expected to be productive for 20 years, after which time the property will be worth about $65,000. The expected annual net income is $35,000, and deposits into a depletion reserve could earn 9.5%, compounded annually. (6 marks)
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12. A pulp company purchases timber rights for 12 years, expecting to earn 15% on the investment. The value of the land after total depletion is estimated to be $85,000, and a depletion reserve is set up at 12%, compounded annually. If the annual net income is $125,000, (a) what is the depleted capital investment, and (b) what will the increase in the depletion reserve be in the 8th year? (8 marks)
(a)
(b)
13. Calculate the capitalized value of land leased for $5,000 per year if money is worth 9.75%, compounded semi-annually. (4 marks)
14. A prospective fitness business investor seeks to know the capitalization cost for a
business for which the initial cost is $135,000, and maintenance and replacement costs will be $9,500 every year. Assume that money is worth 15%. (4 marks)
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Assignment 5
15. Calculate how much would be economically feasible to spend on the overhaul of equipment that has to be replaced every 20 years at a fixed cost of $75,000. The overhaul being considered would take place 4 years before replacement is due, and it would extend the life of the equipment by 3 years. Assume money is worth 10.5%. (6 marks)
16. Calculate the annual investment cost of an asset that originally costs $20,000 and will need replacement parts worth $250 every quarter. Assume money is worth 12.5%, compounded semi-annually. (5 marks)
17. (a) Decide which of the two investments listed below is best if money is worth 10.5%, compounded annually. (b) State the difference in capital costs. (5 marks)
Choice A: Initial cost of $12,000 with a life of 10 years and scrap value of $450
Choice B: Initial cost of $11,600 with a life of 7 years and scrap value of $600
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(a)
(b)
18. Calculate the annual investment cost advantage of the best choice in Problem 17. (2 marks)
19. A company must buy new safety equipment every 10 years, costing $26,000, with
a salvage value of $2850. A new type of equipment is coming on the market soon that will last 10 years and have a salvage value of 13% of the original cost. If money is worth 12.5% annually, compare the two possibilities and identify the highest price the company should pay for the new type of equipment. (4 marks)
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