Question 1

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

EFFECTIVE VERSUS NOMINAL INTEREST RATES

Bank A pays 4% interest compounded annually on deposits, while Bank B pays 3.5% compounded daily.

A) Based on the Effective Interest Rate (EIR) which bank should you use?

B) Could your choice of banks be influenced by the fact you might want to withdraw your funds during the year as opposed to at the end of the year? Assume that your funds must be left on deposit during an entire compounding period in order to receive any interest.

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

1. How large a sum must Sunrise accumulate by the end of year 12 to provide the 20-year, $42,000 annuity?
2. How large must Sunrise's equal annual end-of-year deposits into the account be over the 12-year accumulation period to fund fully Ms. Moran's retirement annuity?
3. How much would Sunrise have to deposit annually during the accumulation period if it could earn 10% rather than 9% during the accumulation period?
4. How much would Sunrise have to deposit annually during the accumulation period if Ms. Morans retirement annuity were a perpetuity and all other terms were the same as initially described? [ 10 marks]