Financial Math Answers

Explain in a paragraph of about 100-150 words when and why would a bond be sold on a premium or discount? You may use graphs, equations, or other aids to assist your explanation.

III. John is currently 25 years old. He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p.a. He also wishes to deposit $X every month into that account so that when he retires at 55, he can withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account?

I. A family buys a house worth $326,000. They pay $75,000 deposit and take a mortgage for the balance at J12=9% p.a. to be amortized over 30 years with monthly payments.

A. Find the value of the mortgage on their house?
B. Find the value of the monthly payment?
C. Find the loan outstanding after making 20 payments?
D. Find the principal repaid in the 21st payment?

John is currently 25 years old. He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p.a. He also wishes to deposit $X every month into that account so that when he retires at 55, he can withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account?

Find the present value of $10,000 received at the start of every year for 20 years if the interest rate is J1 = 12% p.a. and if the first payment of $10,000 is received at the end of 10 years?

III. John is currently 25 years old. He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p.a. He also wishes to deposit $X every month into that account so that when he retires at 55, he can withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account? (10 Marks)

Suppose that ABC Ltd is considering purchasing one of three new processing machines. Either machine would make it possible for the company to produce its products more efficiently. Estimates regarding each machine are provided below: Machine A Machine B Machine C Original cost $79,000 $110,000 $244,000 Estimated life 7 years 8 years 10 years Salvage value Nil Nil $30,000 Estimated annual cash inflows $30,000 $ 60,000 $58,500 Estimated annual cash outflows $ 7,000 $ 35,000 $18,500 A. If the projects cannot be repeated, which machine should ABC Ltd choose based on the NPV criteria at an 8% cost of capital? (9 marks) B. If the projects can be repeated, which machine should ABC Ltd choose based on the NPV criteria at an 8% cost of capital? (6 marks) C. Calculate the internal rate of return for Machine A? [Hint: internal rate of return is the rate which results in a zero NPV using linear interpolation], and discuss 1 drawback of the IRR against the NPV (5 marks)

Suppose that after making 50 payments, the interest rate changes to J2=9% p.a.:

A. Convert the interest rate J2=9% to J12 equivalent (2 marks
B. Assuming that the family seeks to accept the change in interest rates, what would be their new payment based on the new interest rate? (5 marks)
C. Assuming that the family seeks to continue their initial monthly payment calculated in part I, how many full payments would be required to pay off the loan and what would be the final concluding smaller payment one period later? (9 marks

. A family buys a house worth $326,000. They pay $75,000 deposit and take a mortgage for the balance at J12=9% p.a. to be amortized over 30 years with monthly payments.

A. Find the value of the mortgage on their house? (1 mark)
B. Find the value of the monthly payment? (3 marks)
C. Find the loan outstanding after making 20 payments? (4 marks)
D. Find the principal repaid in the 21st payment? (5 marks

Suppose that ABC Ltd is considering purchasing one of three new processing machines. Either machine would make it possible for the company to produce its products more efficiently.
Estimates regarding each machine are provided below:

Machine A Machine B Machine C
Original cost $79,000 $110,000 $244,000
Estimated life 7 years 8 years 10 years
Salvage value Nil Nil $30,000
Estimated annual cash inflows $30,000 $ 60,000 $58,500
Estimated annual cash outflows $ 7,000 $ 35,000 $18,500



A. If the projects cannot be repeated, which machine should ABC Ltd choose based on the NPV criteria at an 8% cost of capital? (9 marks)

B. If the projects can be repeated, which machine should ABC Ltd choose based on the NPV criteria at an 8% cost of capital? (6 marks)

C. Calculate the internal rate of return for Machine A? [Hint: internal rate of return is the rate which results in a zero NPV using linear interpolation], and discuss 1 drawback of the IRR against the NPV (5 marks)