Independent solution

How to solve this Interest Rate Valuation question

Setup

Setup

A nominal interest rate compounds by one plus k/2 each half-year, while nominal discount accumulates by the reciprocal of one minus k/2.

1000(1+k/2)10=921.90(1−k/2)−101000(1+k/2)^{10}=921.90(1-k/2)^{-10}

Model

Model

Equating the two ten-period values and combining their factors produces one minus k squared over four.

(1−k2/4)10=0.9219(1-k^2/4)^{10}=0.9219

Compute

Compute

The positive rate solution is 18%; applying its 9% half-year interest rate to Fund X gives 2,367.36.

k=0.18k=0.18

Answer

Answer

The closest listed common value is 2,370, choice E.

P=1000(1.09)10=2367.36≈2370(E)\boxed{P=1000(1.09)^{10}=2367.36\approx2370\quad\text{(E)}}