Entire Course Review

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^[1] The executor of Sam Jackson’s estate is to divide $880,000 between three charities, the United Way, Heart Fund and Red Cross in the ratio of 6:3:2 respectively. How many dollars will each charity receive?

^[2] A publisher sells its romance novels with chained discounts of 10% and 20%.

1. Find the single equivalent discount rate.
2. The publisher would like to add a third chained discount to bring the overall discount to 31.6%. Find the third chained discount rate.

^[3] An invoice with terms 2/10, 1/20, n/45 for $3,000 dated November l was partially paid by a $1,470 payment on November 10th and a second payment of $495 on November 20th. What is the outstanding balance after the November 20th payment?

^[4] Black Bear Cupcakes received an invoice dated November 28th with terms 1.5/10, n/30 for $8,050. On December 6th, Black Bear mailed a cheque for $4,925 in partial payment of the invoice. What is the outstanding balance after the December 6th payment?

^[5] Chemco Co. sells its products at trade discounts of 25%, 10%. A competitor has been offering products at the same list prices but with trade discounts of 30%, 10%. Chemco wants to beat the competitor’s prices by offering a third trade discount. At least how big must the additional discount rate be to meet this objective?

^[6] What single discount is equivalent to a chain discount of 15%, 10%?

^[7] If we want a single equivalent discount of 19.25% by using chain discounts of 15% and $x$, what must the second discount rate be?

^[8] A furniture manufacturer offers his clients discount rates of 22.5% and 10%.

1. What single rate is equivalent to this series of rates?
2. If a client of this manufacturer paid $1,395 for a sofa, at what price was the sofa listed?

^[9] Find the selling price of an item bought for $1,050.00 if the margin is 30%?

^[10] If a company maintains a margin of 20% on all items it sells, what is the rate of markup?

^[11] The regular selling price of an item sold in a store includes a margin of 60%. During a sale, an item that cost the store $240 was marked down 20%. For how much was the item sold?

^[12].      The net price of an article is $612 after discounts of 15% and 10%. What was the list price?

^[13] An item that cost the dealer $850 less 35%, 20% carries a price tag at a markup of 25% of cost. For quick sale, the item was reduced 25%. What was the sale price?

^[14] Find the cost of an item sold for $2,800 to realize a rate of markup of 40%.

^[15]  An article cost $300 and sold for $450. What was the rate of markup?

^[16] The markup on an item is $50. If the margin was 40%, what was the cost?

^[17] The price of an item is reduced for quick sale from $950 to $760. Compute the rate of markdown .

^[18] You are taking a holiday in Britain. You are taking 850 US dollars with you. How many British pounds can you buy with this money?

Rates:

• 1 USD= 1.38358 CAD
• 1 British pound(£) =$2.21824 CAD

^[19].     A manufacturer of major appliances provides the following information about the operations of the refrigeration division:

• Fixed costs per period are $26,880
• Variable costs per unit are $360
• Selling price per unit is $640, and
• Capacity is 150 units.

Compute the break-even point:

1. in units.
2. as a percent of capacity.
3. in dollars.

^[20] Find the cost-equation for shipping one ton of a product if we know that it costs $500 to ship it a distance of1,000 kilometres and $750 to ship it 2,000 kilometres. Assume that the relationship between cost of shipping and distance shipped is linear. What would it cost us to ship one ton of the product 1,500 kilometres? Check your answer by putting the two points back into the equation.

^[21] The High Tech computer shop assembles and sells computers. After reviewing their accounting data, the following was determined.

• Fixed costs: $100,000 per year
• Variable costs $1,450 per computer
• Selling price per computer: $2,450
• Capacity is 1,000 computers per year

1. How many computers must it sell per year to break even?
2. What is the total yearly sales (revenue) required to break even?
3. Determine the computer shop’s yearly profit if it sells 250 computers per year?
4. How many computers would need to be sold to make a $25,000 profit?
5. If the variable costs increase to $1,600 per computer, what should you increase the selling price to if you want to earn a profit of $25,000 from the sale of 125 computers?

^[22] A small production company has 3 choices when renting a mobile crane for short periods:

• Choice A:It can pay $200 per hour used.
• Choice B: Pay an annual fee of $5,000 and pay only $100 per hour used.
• Choice C: Pay an annual fee of $12,000 and pay only $50 per hour used.

1. Write the cost functions for each alternative.
2. Calculate the points of indifference (where the costs are equal).
   1. between alternative A and B
   2. between alternative B and C
3. Determine the range of hourly usage where the three alternatives would be preferred.

^[23] You take out a loan for $10,000. The most you can afford to pay is $425 per month at the end of every month. If the interest rate on the loan is 7% compounded monthly, how many months will it take you to pay off the loan? (No decimal answers!)

^[24] Kate made $600 monthly deposits at the end of every month for 5 years into an RRSP paying 8% compounded monthly. Immediately after the end of the 5th year the rate is reduced to 6% compounded quarterly.

1. If neither deposits nor withdrawals were made during the next 10 years, how much would Kate have in her account at the end of 15 years?
2. How much interest did Kate earn over the entire 15 year period of time?

^[25] You have just turned 30 years old. Starting today, you will make monthly contributions of $600 into a RRSP for 25 years. One month after your 55th birthday you will begin taking monthly withdrawals with your last withdrawal on your 70th birthday.

1. Find the size of these withdrawals if the interest rate is 6.5% compounded monthly.
2. How much interest did you earn over the entire 45 years?

^[26] Barney wants to start saving for his retirement. Starting today, he will make monthly deposits to his RRSP for 20 years. One month after his last deposit, he wants to withdraw $4,000 per month for 10 years. Assume the invested funds earn 6% compounded monthly for the entire time.

1. How much must Barney deposit into his RRSP per month to achieve his goal?
2. How much interest will Barney earn over the 30 years?

^[27] If you agree to make a payment of $1,500 in 3 months at 6% simple interest, how much money are you borrowing today?

^[28] You borrow $6,000 on November 15, 2021 at 8% simple interest. How much do you owe the bank when you pay off the debt on March 15, 2022? What is the cost of financing?

^[29] You borrowed $3,000 from the bank some time ago at 6% simple interest. You paid off the loan today with one payment of $3,360. How many months ago did you borrow the $3,000?

^[30] A debt of $6,000 was due 6 months ago and a debt of $14,000 is due 5 months from today. Instead, the borrower agrees to make 2 equal payments, to be made 3 months, and 8 months from today, with simple interest allowed at 12%. What is the size of the payments? Use 5 months as the focal date.

^[31] You would like to save to return to school. You deposit $4,000 into a GIC that pays j₄ = 7.44%. You have decided to return to school when your savings grow to at least $6,000. If you make no more contributions, how many years will it take you to reach your goal?

^[32] An investment of $2,000 made 30 months ago is now worth $2,676.45. What nominal rate of interest, compounded semi­ annually, did the investment earn?

^[33] What nominal rate, compounded semi-annually, is equivalent to 12% compounded quarterly?

^[34] Debts of $800 due today and $900 due in 27 months are to be repaid with 2 equal payments, 1 year and 2 years from today. If the interest rate is 9% compounded quarterly, find the size of the payments. Use 2 years as the focal date.

^[35] You are searching for a mutual fund.

• Fund 1 offers a rate of return of 6.4% compounded quarterly.
• Fund 2 offers a rate of return of 6.6% compounded semi­-annually.

Convert all rates to effective rates. Which fund is the better investment?

^[36] You purchase a new car. The dealer offers you terms of 20% down and the remainder financed over three years at an interest rate of 9% compounded quarterly. The cost of the car is $21,640.79.

1. Find the size of your monthly payment if your first payment is due one month after you purchase the car.
2. What is the cost of financing (i.e., how much interest will you pay)?

^[37] A TV set may be purchased on these terms: a down payment of 20% of the selling price is to be made on the date of purchase, followed by 18 monthly payments of $40 each, with the first payment one month after the date of purchase. If the interest rate charged is 10% compounded monthly, what is the cash price (selling price) of the TV set?

^[38] A used car that sells for $15,000 may be purchased by making payments of $500 per month for 3 years with the first payment due the day the car is purchased.

1. What nominal rate of interest, compounded quarterly, is charged?
2. What effective rate of interest is charged?

^[39] You take out a loan for $12,000 with quarterly payments of $806.59 at the end of each quarter. If the interest rate on the loan is 12% compounded quarterly, how many years will it take you to pay off the loan?

^[40] John will purchase an annuity that will pay him $5,000 per quarter for 10 years beginning when he turns 60 years of age. If John’s current age is 45 years and the invested funds will earn 7.0% compounded quarterly, what amount must he invest in the annuity today so he can collect $5,000 per quarter for 10 years with the first payment on his 60th birthday?

^[41] A bursary fund for BCIT honour students is to be funded by a perpetual fund. The fund earns interest at 8% compounded semi-annually and is to pay $2,000 every six months, with the first scholarship paid in six months. Find the size of the initial funding that is required.

^[42] A friend has invested in a bond fund and says she doubled her money in five years. What rate of interest, compounded semi­ annually, did she earn?

^[43] A person can buy a piece of land for $130,000 now or $60,000 now and $100,000 in 5 years. Which option is better if money can be invested at:

1. 6% compounded quarterly?
2. 10% compounded quarterly?

^[44] Meryl just turned 50 years old. She put $50,002 into her RRSP today. She will leave the money in her RRSP until her 65th birthday. She will then purchase a 10-year annuity with the first withdrawal one month later. Use

1. What will be the size of the monthly withdrawals?
2. How much interest did Meryl earn over the 25 years?
3. Meryl has determined that she requires a larger monthly payment than that found in part (a). She would like to receive $2,000 per month. How much additional money must she transfer to her RRSP today so she can collect $2,000 per month instead?

^[45] You invest $4,000 in a mutual fund. Your investment of $4,000 earns the following returns.

What average nominal rate of return, compounded semi­ annually did you earn?

^[46] You purchase a new car. The dealer requires that you put $6,000 down followed by monthly payments of $999 over four years. (The first payment is made one month after you buy the car). The interest rate is 9.9% effective.

1. What is the cash price (selling price) of the car?
2. What is the cost of financing?

^[47] You contribute $2,500 into your RRSP at the end of every quarter for 5 years. If your RRSP earns 8% compounded quarterly, how much interest will you earn in the 5 years?

^[48] A computer that sells for $3,999 may be purchased by making a down payment , plus a series of month-end payments of $225 for one and a half years. If the interest rate is 9% compounded monthly, what is the size of the down payment?

^[49] You are buying a house for $260,000 with a down payment of 20%. The interest rate is 8.5% compounded semi-annually. The mortgage is amortized over 25 years for a 3-year term.

1. Calculate the size of the monthly payment. The lender’s policy is to round payments up to the next whole dollar.
2. How many payments would be required?
3. How much interest will you pay in the first 3 years?
4. How much interest would you pay in the third year only?
5. You make an extra lump-sum payment of $40,000 at the end of 3 years. What is the outstanding balance after this lump-sum payment?
6. When you go to renew your mortgage at the end of
7. 3 years, the rates have fallen to only 5.5% compounded semi-annually for a 3-year term. Find the size of the new payment.
8. The payment determined in part (f) is much smaller than you thought due to the lower rate and lump sum payment. You have decided to increase the monthly payment so that you pay off the remaining balance in only 12 years instead of 22 years. Find the size of the new payment. Round up to the next dollar.
9. Find the size of the final payment.

^[50] A summer cottage, valued at $120,000, may be purchased by paying a $20,000 down payment and financing the balance with a mortgage at 9% compounded semi-annually and monthly payments for 15 years.

1. Find the monthly payment. Round up to the next dollar .
2. How much of the 60th payment pays interest and how much goes toward the principal?
3. After the 100th payment, how much of the original mortgage is still left to be paid?
4. After making 115 payments, what percent of the original debt will have been paid off?

^[51] You are contemplating purchasing a business selling computer software over the Internet.

• • You estimate that the purchase price would be $40,000.
  • Your expenses should be $10,000 per year.
  • You expect annual revenues to be $15,000 for the first two years and $20,000 each year after that.
  • You plan to sell the business at the end of six years and estimate you will get $55,000.
  • Your MARR is 15% effective.
  • Assume all expenses are paid at the beginning of the year and revenues are received at the end of the year. Time diagram is required.

1. What is the IRR? Should you purchase the business? Why or why not?
2. Calculate the NPV. Should you purchase the business? Why or why not?
3. What is the highest purchase price you could pay and still be willing to buy the business?
4. What is the lowest selling price you could tolerate and still be willing to undertake the business? Round to the nearest dollar.
5. You accountant advises you that your annual revenue projections are too high. What is the maximum annual decrease in revenue you could withstand and still have this investment be worthwhile?

^[52] A food concession at an airport has a 7 year life and costs $200,000. Renovations will cost you another $50,000. The concession’s operation is expected to produce net incomes of $60,000 a year. The salvage value of the equipment and ending inventory are expected to total $40,000. Your MARR is 20%.

1. Find the IRR. Would you buy this concession? Why or why not?
2. Find the NPV. Would you buy this concession? Why or why not?
3. By how much does the purchase price of the concession have to fall to make the investment worthwhile? What is the new price?
4. Your accountant tells you your salvage estimate is too low. What is the minimum salvage value you require to make the investment worthwhile?
5. The Canadian government has decided to offer a one-time subsidy to encourage the creation of concession stands at the airport. The subsidy is received one year later. How large of a subsidy would you require to make the investment worthwhile?
6. Your accountant advises you that your projected net incomes are too low. What is the minimum annual increase in revenue you require to make the investment worthwhile?