a. It is said that the Indian who sold Manhattan for $24 was a sharp salesman. If he had put his $24 away at 6% compounded semiannually, it would now be worth more than $9 billion, and he could buy most of the now improved land back! Assume that this seller invested on January 1, 1701, the $24 he received.

Required

1. Use Excel to determine the balance (in billions) of the investment as of December 31, 2021, assuming a 6% interest rate compounded semiannually. 

2. Carry out the same calculation using an 8% annual interest rate, compounded semiannually.

3. What would be the balances for requirements 1 and 2 if interest is compounded quarterly?

4. Assume that the account consisting of this investment had a balance of $9.5 billion as of December 31, 2021. How much would the total amount be on December 31, 2027, if the annual interest rate is 8%, compounded semiannually? 

b. In 2000, a star major-league baseball player signed a 10-year, $252 million contract with the Texas Rangers. Assume that equal payments would have been made each year to this individual and that the owners’ cost of capital (discount rate) was 12% at the time the contract was signed. What is the present value cost of the contract to the owners as of January 1, 2000, the date the contract was signed, in each of the following independent situations?

Required

1. The player received the first payment on December 31, 2000.

2. The player received the first payment on January 1, 2000, the date the contract was signed. (This situationis referred to as an annuity due rather than an ordinary annuity. See www.accountingtools.com/  articles/what-is-an annuity-due.html. In the PV formula in Excel, this situation is handled by setting “type” to 1.)

3. Assuming the owner is in the 45% income tax bracket, recalculate your answer for requirement 1.