## BUSINESS MATHEMATICS

### Part 1: In each question, decide which one of the four choices given will be correct. (14 marks at 2 each)

 1 5 2 6 3 7 4

1) What sum of money will accumulate to \$2000in eight months at 8% pa?

A, \$1898.73       B, \$1899.60         C, \$1898.40        D,\$1900

2) When the periodic interest rate is 0.25%, compounding is monthly, the nominal annual compounding rate is

A, 0.5%       B, 2%        C, 1.0%      D, 5%

3) The Canadian consumer price index (CPI) was approximately 120 at the beginning of 2005. If inflation continues at an average annual rate of 3%, what will the index be at the beginning of 2015?

A, 237.84       B, 165.37         C, 161.27       D, 239.85

#### 4)Calculate the price of a \$500,000, 91-day Province of Nova Scotia Treasury Bill on its issue date if the current market rate of return is 6.773% pa. 金融数学final代考

A, \$ 491697.15       B, \$ 491698.15    C, \$ 491687.15      D, \$ 463697.15

5) An investment promises two payments of \$400, on dates 3 and 5 months from today. If the required return on investment is 8% pa, what is the price of the investment today?

A, \$780        B,\$779.26        C, \$779.23         D, \$780.21

6) An investment promises two payments of \$1400, on dates 3 and 5 months from today. If the required return on investment is 3% compounded monthly, what is the price of the investment today?

A, 2772.18    B, 2872.43   C, 2978.43   D, 2798.12

7) There are three payments: \$700 today, \$1000 due in 1 year, \$1200 due in 3 years. What is the equivalent value 8 months from now if time value of money is 4% compounded annually?

A,\$2800.61     B,\$2800.00         C,\$2801.00           D,\$2801.78

### Part 2:Answer the following questions. Marks are for the answer only. (20 marks at 2 each) 金融数学final代考

1, if \$100,000 will purchase a 20-year annuity paying \$900 at the end of each month, what monthly compounded nominal rate of interest will the invested funds earn?

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2, rounded to the nearest month, how long will it take end-of month deposits of \$150 to accumulate \$10,000 in an investment account that earns 4.5% compounded monthly?

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3, A perpetuity is to pay \$5000 at the end of every six months. How much  money is required to fund the perpetuity if the money can be invested to earn 7% compounded semiannually?

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4, If Justin contributes \$1800 to his RRSP on February 1, 2000, and every six months thereafter, up to and including February 1, 2018, what amount will he accumulate in the RRSP at August 1, 2018? Assume that the RRSP will earn 6.5% compounded semiannually?

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#### 5, What maximum annual withdrawal will a \$100,000 fund earning 7% compounded annually sustain for 20 years if the withdrawals are made at the beginning of each year? 金融数学final代考

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6, What maximum annual withdrawal will a \$100,000 fund earning 7% compounded annually sustain for 20 years if the withdrawals are made at the end of each year?

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7, A \$100,000 loan and \$50,000 loan both have the same interest rate and the same amortization period (10 years). Will the monthly payment on the \$100,000 loan be double the monthly payment on the \$50,000 loan? (Yes or no)

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8, In order to accumulate \$100,000 after 25 years, calculate the amount that must be invested at the end of each year at 6% compounded annually.

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9, Megan purchased a recreational vehicle for \$4,000 down, with the balance to be paid by 60 blended monthly-end payments of \$400 including interest at 5% compounded monthly. What was the purchase price of the vehicle?

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10, A \$7500 item is paid for by end-of-month payments of \$400. The interest rate charged is 6% compounded monthly. What is the number of payments?

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### Part 3: calculation (66 marks) 金融数学final代考

1, (4marks) An interest rate of 10% compounded quarterly is equivalent to what nominal rate of interest compounded Semiannually?

2, (8 marks) (Only Financial calculator method) A two-level retirement annuity will pay \$2000 per month for the first 10 years and \$3000 per month for the next 15 years.What is the present value, 1 month before the first payment, of the entire stream of annuity payments? Money can earn 7.5% compounded monthly.

3, (8 marks) (Only Financial calculator method) A four-year \$7000 promissory note bearing interest at 8% compounded monthly was discounted 18 months after issue to yield 6% compounded quarterly. What were the proceeds for the sale of the note?

#### 4, (4 marks)What is the effective rate of interest corresponding to 10.5% compounded monthly? 金融数学final代考

5,(4 marks) An investor purchased \$250,000 in 364-day T-bills 315 days before maturity to yield 4.34%. He sold the T-bills 120 days later to yield 3.92%.

1) How much did the investor pay for the T-bills?

2) For how much did the investor sell the T-bills?

1. 6. (30 marks) (only retrospective method, only financial calculator method)

Justin borrowed \$6000 at 12.5% compounded monthly and agreed to repay the loan in equal quarterly payments over four years.

A, how much of the fifth payment will be interest?( 6 marks)

B, what will be the principal repaid by the 11th payment? ( 6 marks)

C, how much interest will be paid by payment 5 to 12 inclusive? (7 marks)

D, how much will the principal be reduced in the second year? (6 marks)

E, what will be the final payment? (5 marks)

7, (8 marks) On March 20, 2000, Westcoast Transmission issued 20-year bonds having a 8% coupon rate.

A), At what price did \$1000 face value bonds trade on July 10, 2014, if the required return was 8.2% compounded semiannually?

B), how much of that price was interest that had accrued in favor of the previous owner since the most recent interest payment date?

C), what price would the financial press and securities brokers have quoted for these bonds on July 10, 2014?