In the summer of $1994$, a couple was going through their attic and found a $\$1000$ bond issued by the State of Nevada in $1865$. It read, “Pay to the Bearer” (whoever has possession). States issue bonds when they need to borrow money. In $1865$, Nevada was a new state and in great need of cash, so it issued this bond at an interest rate of $24\%$ compounded annually.

1. Do you think it would have been possible to cash in this bond?

   Hint (a):

   How many years has it been since the bond was issued? Do you think the state could pay that much?

2. If $\$1000$ were invested in $1865$ at an interest rate of $24\%$ compounded annually, how much would the investment be worth in $1994?$

   Hint (b):

   Use to find the worth of the investment.

   More Help (b):

   A $= 1{,}000$  $r = 0.24$  $n = 129$

   Answer (b):

   The investment is worth about $$1.126 · 10^{15}$.

3. What is the place value of the first digit in the answer to part (b)?

   Answer (c):

   The first digit is in the quadrillion place.

4. Would the amount be significantly different if was compounded continuously instead?

   Answer (d):

   $A ≈ $2.791 · 10^{16}$, or about $2.68 · 10^{16}$ dollars more.