Independent solution

How to solve this Nominal Discount Equivalence question

Setup

Setup

Use the quoted accumulation relationship to solve for the nominal annual discount rate d. Semiannual and quarterly discount conventions must be kept in their own period lengths.

(1−d/2)−4=3938(1−d/4)−4(1-d/2)^{-4}=\frac{39}{38}(1-d/4)^{-4}

Model

Model

The equality of four-period factors gives d = 10%. Convert the semiannual nominal discount quote to an annual effective interest rate through its discount factor.

d=0.10d=0.10

Compute

Compute

The annual accumulation is (1 − 0.10/2) to the power −2, giving i = 0.108, or 10.8%.

i=(1−0.10/2)−2−1=0.108i=(1-0.10/2)^{-2}-1=0.108

Answer

Answer

The calculation gives 10.8% for nominal discount equivalence, matching published choice C.

i=10.8%(C)\boxed{i=10.8\%\quad\text{(C)}}