Suppose that there is a bank that is offering to lend and/or borrow money at an interest rate of 8% (regardless of the time-to-maturity of the loan). Further suppose that there is a two-year coupon...

Suppose that there is a bank that is offering to lend and/or borrow money at
an interest rate of 8% (regardless of the time-to-maturity of the loan).
Further suppose that there is a two-year coupon bond trading with a face
value of $100 and a coupon rate of 5% trading in the market. Price the bond
using an explicit no-arbitrage argument.

Question: Suppose that the bank stated previously is still around. Consider
a gold mine that will produce annual cash flows of $100 (with certainty)
for five years starting in two years, i.e. from t = 2 to t = 6. What is the
arbitrage-free price of the gold mine?