1. How many years will it take $106,000 to grow to $218,000 at 1.1% annual interest (compounded annually) if interest only accrues at the end of the year? Your answer should be an integer.
2. Suppose you have the alternative of receiving either $26,000 at the end of 10 years or P dollars today. You do not need the money, so you could deposit the P dollars in a bank that pays 6.5 % interest. What value of P would make you indifferent in your choice between P dollars today and receiving $26,000 at the end of 10 years?
3. A professional baseball player signs a contract for $164 million to play with a team for 7 years. He and his team agree that the contract will be spread out so that the player is paid beyond the 7 years. The payment plan for the contract is as follows:
$16 million each year for years 1 through 7.
$3.2 million each year for the next 7 years.
$1.0 million each year for the next 7 years.
You should assume that the baseball team will pay the player annually at the end of each year and that he will receive the first $16 million at the end of the first year. The player receives money for 21 years.
The player had previously rejected a contract that would have paid $153 million for 7 years in which the $153 million would be paid in 7 equal installments (i.e., $21.86 million per year). The first payment would be made at the end of the first year.
Assume the player will invest every dollar that he receives in an account that pays 5.8% interest compounded annually. Enter the amount in millions of dollars of the contract that would result in the most money at the end of 21 years for the player.
4. The interest rate is 13.3% compounded annually. Consider the following cash flow.
Year 0: (-$44)
Year 1: $0
Year 2: $92
Year 3: $137
Year 4: $173
Year 5: $252
Find the value of A --where you receive A 6 times (years 0-5)--that is economically equivalent to the preceding cash flow. HINT: This is different than the normal equal payment series because you are also receiving A in year 0.
5. Consider the following deposits made into a savings account that earns a constant interest compounded annually. 'An' represents the actual deposits made at the end of year n. 'Pn' represents the present value of the deposit in year n. The present value 'Pn' of $810 in year 2 is $733.70. Assuming there are only 4 deposits made, calculate the total amount in the savings account at the end of year 4.
'An' in $ (Years 0 through 4):
0
600
810
170
0
6. What is the future value at the end of year 5 of a series of 3 deposits? The first deposit occurs at the end of year 3 and is $1100. The remaining deposits increase by $220/year (so the last deposit will be $1540 and will occur at the end of year 5) . Assume i = 7.2% compounded annually.
7. Joe's starting salary as a mechanical engineer is $84,000. Joe is planning to place a total of 11.7% of his salary each year in mutual funds. Joe expects a 4.1% salary increase each year for the next 25 years of employment. If the mutual fund will average 6.2% annual return over the course of his career, how much money can Joe expect at retirement?