Answer to Question #137589 in Financial Math for sarah

Question

Robert Johnson owns a farm and breeds race horses. To purchase three thoroughbreds,
he signs a 180-day note with a maturity value of $ 255,000 and proceeds of $ 243,137.50.
Find (a) the discount and (b) the true (or effective) rate .

Answer 1

(a)

The discount is $3\cdot(255000-243137.50)=35587.50$  ($).

(b)

180 days is 6 month, the nominal rate is $\frac{255000-243137.50}{243137.50}≈0.04879=4.879\%$,

so the true (or effective) rate is $(1+\frac{0.04879}{6})^6-1≈0.04979=4.979\%$.