PRESENT VALUE AND LOAN ELIGIBILITY You have saved $4,000 for a down payment on a new car. The largest monthly payment you can afford is $350. The loan would have a 12% annual interest based on end-of- month payments. What is the most expensive car you could afford if you finance it for 48 months? For 60 months? [4 marks] Question 2 TIME TO ACCUMULATE A GIVEN SUM John wishes to determine how long it will take an initial deposit of $100000 to double. a.) If John earns 10% annual interest on the deposit, how will it take for him to double his money. [2 marks] b.) How long will it take if he earns 6% annual interest rate. [2 marks] c.) Based on your findings in a and b, indicate what relationship exists between the interest rate and the amount of time its take for him to double his money [3 marks] Question 3 Time to repay installment loan. Theresa wishes to determine how long it will take to repay with initial proceeds of $250000 where end of year installment payments of $20000 are required. a.) If Theresa can borrow at an interest rate of 12%, how long will it take for her to repay the loan fully. [2 marks] b.) How long will it take if she earns 6% annual interest rate? [ 2 marks] c.) Based on your findings in a and b, indicate what relationship exists between the interest rate and the amount of time its take for her to repay the loan fully. [3 marks] Question 4 NOMINAL INTEREST RATE AND EXTENDING CREDIT As a jewelry store manager, you want to offer credit, with interest on outstanding balances paid monthly. To carry receivables, you must borrow funds from your bank at a nominal 6%, monthly compounding. To offset your overhead, you want to charge your customers an EIR that is 2% more than the bank is charging you. What annual interest rate should you change your customers? [ 3 marks] Question 5 ; LOAN RATE OF INTEREST John has been shopping for a loan to finance the purchase of a car. He has found three possibilities that seem attractive and wishes to select the one with the lowest interest rate. The information available with respect to each of the three 5000 loans is shown in the table below. a) Determine the interest associated with each of the loans b) Which loan should John take? [6marks] Question 6 FUTURE VALUE OF UNEVEN CASHFLOW You want to buy a house within 3 years, and you are currently saving for the down payment. You plan to save $5000 at the end of the first year, and you anticipate that your annual savings will increase by 10% annually thereafter. Your expected annual return is 7%. How much would you have for a down payment at the end of year 3 ? Question 7 AMORTIZATION SCHEDULE A. Joan Williams borrowed $15000 at 14% annual rate of interest to be repaid over three years. The loan is repaid over three equal end of year payments. i.) Calculate the annual end of year payments ii) Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments B. What percentage of the payment represents interest and what percentage represents principal for each of the 3 years? Why do these percentages change overtime? [8marks] Question 3 RETIREMENT SAVINGS AND PLANNING Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Jill Moran. Ms. Moran by contract will retire at the end of exactly 12 years. Upon retirement, she is entitled to receive an annual end-of-year payment of $42,000 for exactly 20 years. If she dies prior to the end of the 20 -year period, the annual payments will pass to her heirs. During the 12-year "accumulation period" Sunrise wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 9% interest. Once the 20 -year "distribution period" begins, Sunrise plans to move the accumulated monies into an account earning a guaranteed 12% per year. At the end of the distribution period, the account balance will be zero. Note that the first deposit will be made at the end of year 1 and that the first distribution payment will be received at the end of year 13 . Required a. How large a sum must Sunrise accumulate by the end of year 12 to provide the 20 -year, $42,000 annuity? b. How large must Sunrise's equal annual end-of-year deposits into the account be over the 12year accumulation period to fund fully Ms. Moran's retirement annuity? c. How much would Sunrise have to deposit annually during the accumulation period if it could earn 10% rather than 9% during the accumulation period? d. How much would Sunrise have to deposit annually during the accumulation period if Ms. Moran's retirement annuity were a perpetuity and all other terms were the same as initially described? [ 10 marks]
