Independent solution

How to solve this Force of Interest to Nominal Discount Conversion question

Setup

Setup

Integrate the time-varying force over the stated four-tenths-year interval.

A=exp⁡(∫2.02.4210−t dt)=(87.6)2A=\exp\left(\int_{2.0}^{2.4}\frac{2}{10-t}\,dt\right)=\left(\frac8{7.6}\right)^2

Model

Model

Let d be the nominal annual discount rate with one conversion every two years. The two-year discount is 2d.

A=(1−2d)−0.4/2=(1−2d)−0.2A=(1-2d)^{-0.4/2}=(1-2d)^{-0.2}

Compute

Compute

Equate accumulation factors and solve.

(1−2d)−0.2=(87.6)2(1-2d)^{-0.2}=\left(\frac8{7.6}\right)^2
d=0.2006315d=0.2006315

Answer

Answer

The nominal discount rate is approximately 20%, choice A.

d≈20.1%(A)\boxed{d\approx20.1\%\quad\text{(A)}}