Why do I mix up bond price, yield, and duration formulas?

They all use the same underlying bond, but they answer different questions.

• Price asks: what is the present value of the cash flows?
• Yield asks: what discount rate makes the price equal the present value of cash flows?
• Duration asks: how sensitive is the price to a small yield change?

Think of price as valuation, yield as the implied rate, and duration as risk. If the prompt gives cash flows and a required return, price the bond. If it gives price and asks for return, solve yield. If it gives duration and a yield move, estimate the price change.