Question

It is said that the Indian who sold Manhattan for $26 was a sharp salesman. If he had put his $26 away at 5% compounded semiannually, it would now be worth more than $8 billion, and he could buy most of the now-improved land back! Assume that this seller invested on January 1, 1701, the $26 he received. (Enter amounts in whole dollars, not in billions. Round final answers to nearest whole dollar amount.)

Required:

1. Use Excel to determine the balance of the investment as of December 31, 2018, assuming a 5% interest rate compounded semiannually. (Hint: Use the FV function in Excel.)

2. Use Excel to determine the balance of the investment as of December 31, 2018, assuming an 6% annual interest rate, compounded semiannually. (Hint: Use the FV function in Excel.)

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 $8.5 billion as of December 31, 2018. How much would the total amount be on December 31, 2024, if the annual interest rate is 6%, compounded semiannually?

Answer 1

1.
=FV(5%/2,2*(2019-1701),0,-26)=171930029.279973

2.
=FV(6%/2,2*(2019-1701),0,-26)=3797067000.35579

3.
=FV(5%/4,4*(2019-1701),0,-26)=189432245.721439

4.
=FV(6%/4,4*(2019-1701),0,-26)=4362938477.70207

5.
=FV(6%/2,2*(2024-2018),0,-8.5*10^9)=12118967538.1925