MATH1091_Aaditya_Sehgal_Assignment_1.docx

MATH 1091: Business Mathematics 1 Student’s Name: Aaditya Sehgal (T00753501) Calculator make and model: Basic Calculator Assignment 1 Total marks: 100 1. Complete the sentences below. (5 marks) (a) Compensation for lending money that is based on one fixed sum is called: Fixed interest (b) The formula to find the maturity value of a simple interest loan is: Maturity Value = principal + (principal x Rate x Time) (c) A transferable paper that commits the signer to pay the amount shown is called: Promissory note (d) To calculate the legal due date of a Canadian promissory note you must: To the date of signing, add the number of days specified in the promissory note. (e) A loan arrangement carrying a fluctuating rate of interest, which can be terminated at any time by either borrower or lender, is called: Variable Rate Loan 2. Find the exact time between March 10 and October 17. (1 mark) 231 days; 5544 hours 3. What is the maturity date of a 90-day debt incurred on September 14? (1 mark) December 13 4. What is the legal due date of a 120-day promissory note issued on April 6? (1 mark) August 4 5. Calculate the simple interest payable on a 6-month loan of $60,000 if the interest rate is 16.5%. (1 mark) $4950 TRU Open Learning

2 Assignment 1 6. Calculate the interest payable on a 60-day promissory note for $4500 if the rate is 12% and the note was signed on July 2. (2 marks) Interest= PxRxT P= principal; R= rate; T=time Interest= 88.219 So, the interest payable on a $4500 60-day promissory note at 12% is roughly $88.22. 7. What principal will earn $600 interest at 14% in 7 months? (2 marks) P=Interest/RxT P= 7373.74 the principal that will earn $600 interest at 14% in 7 months is approximately $7,373.74. 8. How long will it take $1,200 to earn $120 at 10%? (2 marks) Time= Interest/PxR Time= 1 year 9. What rate of interest could earn $250 on a principal of $3,000 in 300 days? (2 marks) T=300/365= 0.8219 R=interest/Pxt Rate= 0.1013 the rate of interest that could earn $250 on a principal of $3,000 in 300 days is approximately 10.13%. 10. What will be the amount payable on the legal due date of a 6-month promissory note for $5,000 signed on August 12 with interest at 13%? (3 marks) Interest= PxRxT = 5000x13%x6/12 TRU Open Learning

MATH 1091: Business Mathematics 3 =325 Amount payable= 5000+325 = 5325 The amount payable of a 6-month promissory note for $5,000 signed on August 12 with 13% interest would be $5,325. 11. Determine the cost of financing a demand note signed on July 15 for $3,550 if the interest rate was 11.5% until the first part-payment of $1,350 on November 11, after which it went up to 12.5% until the note was paid in full on December 25? (4 marks) P= 3550 R!= 11.5%- 0.115 T!=119 days (July 15 to November 11) Interest!= 3550x0.115x119/365 = 133.0895 Second period- November 11- December 25 T= 45/365 Interest= 3550x0.125x45/365 = 54.7140 Total Interest= 133.0895+54.7140 = 187.8035 TRU Open Learning

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4 Assignment 1 12. Use the declining-balance method to calculate the final payment needed on July 7 to clear out a 14.5% debt of $5,500 incurred on March 20 if the following partial payments were made: $1,500 on May 4 and $2,000 on June 6. (5 marks) * Doubt on how to do this question * i am not sure if this is the right way.. Initial payment = $5500 1 ST partial payment= $1500 may 4 Remaining balance = 5500-1500 = $4000 Interest = Remaining balance x R x T = 4000 x 0.145 x 1/12 = $48.34 2 ND Partial payment = $2000 on June 6 Remaining balance = $4000 - $2000 = $2000 Interest = 2000 x 0.145 x 1/12 = $24.17 Final Payment = 2000 + 24.17 = $2024.17 13. What was the cost of the loan described in Problem 12? (2 marks) Total cost = Initial debt + Interest for may 4-june 6 + interest for June 6-July 7 Total cost = 5500 + 48.34 + 24.17 = $5572.51 14. Sean plans to sell a property in Kelowna expected to have a value of $115,000 in 5 years. If money is worth 12.5% simple interest, what is a fair price to pay for the property today. Ignore local taxes. (3 marks) P=F/1+RxT P= present value F= Future Value = 115,000 P= 115000/1+12.5%x5 = 70,769.23 TRU Open Learning

MATH 1091: Business Mathematics 5 15. John lent a friend $5000 at 10% and received $500 in interest. How long did John’s friend have use of the money? (3 marks) T=Interest/PxR T= 500/5000x0.10 T= 1 year 16. After 2 years, you receive an offer of $110,000 for the property purchased in Problem 14. Would you accept the offer? Assume that you have paid $500 a year for land taxes for each year you have held the property. For full marks, make sure you show your work. (4 marks) Annual Land Tax for 2 years= 2x500=1000 Initial investment+ annual land tax= 70,769.23+1000= 71,769.23 It appears to be a good deal because the offer of $110,000 is larger than the entire investment of $71,769.23. Accepting the offer may be an acceptable decision if your primary goal is to maximize profit. 17. Calculate the present value of a debt that will amount to $1518.33 in 4 months, if simple interest is charged at 12%. (2 marks) P=F/1+RxT P= 1518.33/1+0.12x4/12 P= $1460.56 18. What is the value on June 15 of a non-interest-bearing promissory note of which the face value is $13,000 and which matures on December 13, if money is worth 17%? (3 marks) Same Formula as used in the above question P=13000/1+0.17x0.078125 TRU Open Learning

6 Assignment 1 P= $12028.37 19. What would be the value of a $14,000 debt after 6 months if money is worth 17%? (2 marks) F=Px(1+RxT) F= 14000 x (1+0.17x6/12) F= $15,190 20. If money is worth 16%, calculate the single equivalent payment 9 months from now of two debts: $300 due 2 months ago and $500 due in 1 year. Use 9 months from now as the focal date. (4 marks) P1=300/1+0.16x11/12 P2= 500/1+0.16x9/12 P1= 231.50 P2= 446.43 Single equivalent payment= P1+P2 = $677.93 21. Find the size of two equal payments—one due now and the other in 8 months— that are to replace three original debts of $2000 each due 6, 4, and 2 months ago. Use a rate for money of 12% and now as the focal date. (5 marks) P1= 2000/1+0.12x6/12 = $1886.79 P2= 2000/1+0.12x4/12 = $1923.08 P3= 2000/1+0.12x2/12 = $1960.78 Total present value= P1+P2+P3 = $5770.65 Size of each payment= Total present value/1+0.12x8/12 = $2551.84 So, the total present value of the three debts is about $5770.65, and each of the two equal payments is about $2551.84. TRU Open Learning

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MATH 1091: Business Mathematics 7 22. You own two debts—$1500 due 1 month ago to National student loans and $1,800 due 3 months ago to Provincial student loans—are to be replaced by three new payments: one of $1000 due now, one of $800 due in 4 months, and the reminder in 8 months. Find a size of the final payment if money is worth 15%. Use now as a focal date. ( 5 marks) Pnational= 1500/1+0.15x1/12 = $1480.49 Pprovincial= 1800/1+0.15x3/12 = $1734.69 Payment of $1000 due now: Pnow= 1000/1+0.15x0/12 = $1000 Payment of $800 due in 4 months: P4m= 800/1+0.15x4/12 = $761.90 Remaining payment due in 8 months: Remaining debt = Total original debt – (Pnational+Pprovincial+Pnow+P4m) = (1800+1500) – ( 1480.49+1734.69+1000+761.90) = 10.92 P8months = remaining debt = 10.92 Size of final payments = P8m = 10.92 23. Find (a) the proceeds and (b) the simple discount of a 3-month, non-interest- bearing note signed on July 10 with a face value of $154,000 if discounting occurs at 13% simple interest on August 24. (4 marks) I=PxRxT (a) P = $154,000 R= 0.13 T= 3/12 I = 154000x0.13x3/12 = $5005 A(proceeds) = P-I = 154000-5005 = $ 148,995 (b) Simple discount is the interest amount i.e $5005 TRU Open Learning

8 Assignment 1 24. Find the proceeds from a $8,000 note that matures on March 5 if it is discounted on January 20 at 13%. Assume no grace. (3 marks) No. of days from Jan 20 to March 5 is 45 days I = 8000x0.13x45/365 = 126.5753 Proceeds (A) = P-I = 8000- 126.5753 = $7873.42 So, the proceeds from $8000 note discounted on Jan 20 at 13% is approximately $7873.42 25. Calculate the simple discount on a 12%, 3-month promissory note for $1000 that was signed on September 6 and discounted at 13% simple interest on October 10. (4 marks) So for 34 days (September 6 – October 10) I = PxRxT = 1000x0.12x34/365 = 9.99 As a result, the simple discount on a $1,000 12% 3-month promissory note signed on September 6 and discounted at 13% simple interest on October 10 is roughly $9.99. 26. If a 120-day, $15,000 note earning 14% simple interest is discounted at 17%, 60 days before its legal due date, what are the proceeds? (4 marks) I=PxRxT = 15000 x 0.14 x 60/365 = $573.15 A = P-I = 15000 – 573.15 = $14426.85 So, the revenues from the discounted note are about $14,426.85, which is a 120-day, $15,000 note earning 14% simple interest discounted at 17% 60 days before its legal due date. 27. Suppose that you decide to discount a $225,000 note you are holding by selling it to a buyer on May 15, which would be 5 months before it is due. If the discount rate is 17.5%, what will the proceeds of the sale be? (3 marks) TRU Open Learning

MATH 1091: Business Mathematics 9 Number of days from the due date to the discount date = 5×30 days = 150 days I = PxRxT = 225000x 0.175 x 150/365 = 20520.55 A=P-I = 225000 – 20520.55 = 204479.45 So, the proceeds from discounted note are approximately $204,479.45 28. Metchosin Tractor purchased a patent on a piece of equipment for $1.5 million and agreed to pay the full amount in 15 years, plus interest. After 8 years, Metchosin Tractor is doing so well that it decides to repay the full patent cost. If money is worth 6% simple interest, how much should Metchosin Tractor offer the company it purchased the patent from to settle the outstanding debt? (4 marks) I = PxRxT = 1.5 million x 0.06 x 8 = 720,000 A= P+I = 1.5 million + 720,000 = 2,220,000 So, Metchosin Tractor should offer $2,220,000 to settle the outstanding debt for the patent after 8 years, assuming 6% simple interest. 29. You are thinking about buying a new car. The sales associate tells you that you can drive away with the car today if you pay $13,000 now and $15,000 in 2 years. If you know that the company charges 26% interest on outstanding balances, what should the cash price be for the car today? (5 marks) P=F/1+RxT P= 15000/1+0.26x2 = $9868.42 30. The car sales associate in Problem 29 says that there is a special on today. If you pay cash, you can buy the car for $24,000, a savings claimed to be of $4,000. Would you accept the offer? Why or why not? (6 marks) TRU Open Learning

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10 Assignment 1 Lets compare the cash price offered today with the future cost if i choose the financing option: Cash price today: $24000 Future value = 13000 (paid today) + 15000 (in 2 years) = $28000 Savings = Future value – Cash price today = $4000 This matches the statement of claimed savings being $4000 As seen above, the cash price provided today is less than the future cost under financing, taking the cash offer would result in saving $4000, according to the sales associate. Therefore, it seems like a reasonable offer, and is considerable to accept. TRU Open Learning

MATH 1091: Business Mathematics 11 31. A couple wants to set aside sufficient money for their daughter to attend college. The cost of college is expected to be $20,000 a year. How much money would need to be placed in an account today that pays 10% simple interest in order for the interest from the account to be sufficient to pay the annual cost of attending college? (5 marks) P=F/1+RxT P= 20000/1+0.10x1 = $18181.82 In order to ensure that the interest from the account is sufficient to meet the annual cost of attending college, the couple would need to invest approximately $18,181.82 in an account today at a 10% simple interest rate, assuming one year of interest accrual before the college fees are due. TRU Open Learning