Planning for:University Victor and Jasmine Gonzalez were discussing how to plan for their three university education. Stephen turned 12-years old in April, Jack turned 9 in ng sond and Danny turned 7 in March. Although university was still a long way off for t Victor and Jasmine wanted to ensure enough funds were available for their st Victor and Jasmine decided to provide each son with a monthly allowance would cover tuition and some living expenses. Because they were uncertain about th boys' finding summer jobs in the future, Victor and Jasmine decided their sons receive the allowance at the beginning of each month for four years. The assumed that the costs of education would continue to increase. Stephen would receive an allowance of S1000 per month starting September Jack would receive an allowance that is 8% more than Stephens allowan the year he turns 18 ce. He beginning of t that would also receive it at the beginning of September 1 of the year he turns 18 Danny would receive an allowance that is 10% more than Jack's at the b September of the year he turns 18. Victor and Jasmine visited their local bank manager to fund the investmen would compensate the boys' allowances for university. The bank manager suggested an investment paying interest of 4.0% compounded monthly, from now until the three boys had each completed their four years of education. Victor and Jasmine thought this sounded reasonable. So on June 1, a week after talking with the bank manager, they deposited the sum of money necessary to finance their sons' post-secondary educations QUESTIONS 1. How much allowance will each of the boys receive per month based on their par- ents' assumptions of price increases? 2. (a) How much money must Victor and Jasmine invest for each son on June 1 to provide them the desired allowance? (b) Create a timeline of events for each of the sons, (c) What is the total amount invested on June 1? Vehicle Cash-Back Ince Karim Soltan is shopping for a new vehicle, and has noticed that man facturers are offering special deals to sell off the current year's vehicles bfan. models arrive. Karim's local Ford dealership is advertising 3.9% financin months (ie., 3.9% compounded monthly) or up to $4000 cash back on selected a full 48 y vehidl is to sell off the current year's vehicles befor the new licence, and dealer preparation. This vehicle qualifies for $1800 cashbackifKaei cash for the vehicle. Karim has a good credit rating and knows that he couldr vehicle loan at his bank for the full price of any vehicle he chooses. His other to take the dealer financing offered at 3.990 for 48 months The vehicle that Karim wants to purchase costs $24 600 includin k if Karim pays arran option is Karim wants to know which option requires the lower monthly payment. Heknowe he can use annuity formulas to calculate the monthly payments QUESTIONS 1. Suppose Karim buys the vehicle on July 1. What monthly payment must Karim make if he chooses the dealer's 3.9% financing option and pays off the loan over 48 months? (Assume he makes each monthly payment at the end of the month and his first payment is due on July 31.) 2. Suppose the bank offers Karim a 48-month loan with the interest compounded monthly and the payments due at the end of each month. If Karim accepts the bank loan, he can get $1800 cash back on this vehicle. Karim works out a method to calculate the bank rate of interest required to make bank financing the same cost as dealer financing. First, calculate the monthly rate of interest that would make the monthly bank payments equal to the monthly dealer payments. Then calculate the effective rate of interest represented by the monthly compounded rate. If the financing from the bank is at a lower rate of interest compounded monthly, choose the bank financing. The reason is that the monthly payments for the banks financing would be lower than the month payments for the dealer's 3.9% financing (a) How much money would Karim have to borrow from the bank to pay ca for this vehicle? (b) Using the method above, calculate the effective annual rate of inte terest and the nominal annual rate of interest required to make the monthly payments bank financing exactly the same as for dealer financing Suzanne had a summer job working in the business office of Blast-It T local chain of home electro heard she had the profitability of two new large-screen TVs. He plans for the two new models to attract customers to his stores. He wants to heavily promote the more profitable TV nics stores. When Michael lacobssen, the owner of the chain, completed one year of business courses, he asked Suzanne to calculate to offer a special payment plan When Michael gave Suzanne the information about the two TVs, he told her to ignore all taxes when making her calculations. The cost of TV A to the company is $1950 and the cost of TV B to the company is $2160, after all trade discounts have been taken. The company plans to sell TV for a $500 down payment and $230 per month for 12 months, beginning 1 month from the date of the purchase. The company plans to sell TV B for a $100 down payment and $260 per month for 18 months, beginning I month from the date of purchase. The monthly payments for both TVs reflect an interest rate of 15.5% compounded monthly Michael wants Suzann e to calculate the profit of TV A and TV B as a percent of s cost to the company. To calculate profit, Michael deducts overhead (which he lates as 15% of cost) and the cost of the item from the selling price of the item. When he sells items that are paid for at a later time, he calculates the selling price as the cash value equals the down payment plus the the TV cash value of the item. (Remember that present value of the periodic payments.) Suzanne realized that she could calculate the profitability of each TV by using her knowledge of ordinary annuities. She went to work on her assignment to provide Michael with the information he requested. QUESTIONS 1. (a) What is the cash value of TV A? Round your answer to the nearest dollar (b) What is the cash value of TV B? Round your answer to the nearest dollar. 2. (a) Given Michael's system of calculations, how much overhead should be assigned to TV A? (b) How much overhead should be assigned to TV B 3. (a) According to Michael's system of calculations, what is the profit of TV A as a percent of its cost? (b) What is the profit of TV B as a percent of its cost? (c) Which TV should Suzanne recommend be more heavily promoted? suppliers of each model gave the company new volume discounts. For TV A, Blast-It received a discount of 9% off its current cost, and for TVB one of 6%. The special payment plans for TV A and TV B will stay the same. Under these new conditions, which TV should Suzanne recommend be more heavily promoted? 1. Three months later, due to Blast-It's successful sales of TV A and TV B, the ESTUDY After reading consumer car guides and receiving advice from family and friends, Aysha has chosen the new car she wants to purchase. She now wants to research her financing options to choose the best way to pay for the car Aysha knows that with taxes, licence, delivery, and dealer preparation fees, her car will cost $17 650. She has saved $7500 toward the purchase price but must borrow the rest. She has narrowed her financing choices to three options: dealer financing, credit union financing, and bank financing. The car dealer has offered 48-month financing at 8.5% compounded monthly. (ii) The credit union has offered 36-month financing at 9% compounded quarte (i) rly. It has also offered 48-month financing at 9.3% compounded quarterly (iii) The bank has offered 36-month financing at 8.8% compounded semi-a It has also offered 48-month financing at 9.1% compounded semi-annually. Aysha desires the financing option that offers the best interest rate. However, she also wants to explore the financing options that allow her to pay off her car loan more quickly QUESTIONS 1. Aysha wants to compare the 48-month car loan options offered by the car dealer, the credit union, and the bank. (a) What is the effective annual rate of interest for each 48-month option? (b) How much interest will Aysha save by choosing the best option as against th worst option? 2. Supp ose Aysha wants to try to pay off her car loan within three years. (a) What is the effective annual rate of interest (b) How much interest wil Aysha save by choosing the better option? for both of the 36-month options? et a car loan today, what are the rates of interest for 36-month s? Are car dealers currently offering better interest rates than 3. If you wanted to g and 48-month term the banks or credit unions? If so, why