Final answer:
To find the annual nominal rate compounded daily for a bond with an annual yield of 3.7%, use the formula A = P(1 + r/n)^(nt). Substitute the given values and solve for r.
Step-by-step explanation:
To find the annual nominal rate compounded daily for a bond with an annual yield of 3.7%, we can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal, r is the annual nominal rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, we have an annual yield of 3.7%, so the annual nominal rate would be 3.7%. The bond compounds daily, so n = 365. We'll assume a 1-year bond for simplicity, so t = 1.
Plugging in the values, we get A = P(1 + 0.037/365)^(365*1). Solving for r, we have 1 + r/365 = (A/P)^(1/(365*1)).
Rearranging the equation, we find r/365 = (A/P)^(1/(365*1)) - 1. Multiplying both sides by 365, we get r = 365[(A/P)^(1/(365*1)) - 1].
Substituting the values for A and P from the given information, we have r = 365[(2777.80/3000)^(1/365) - 1]. Evaluating this expression gives us the annual nominal rate compounded daily for the bond.