Independent solution

How to solve this Geometrically Increasing Coupons question

Setup

Setup

Convert the 4% annual effective yield to the equivalent half-year yield j. The twelve coupons increase geometrically by 2% each period.

j=1.04−1=0.019804j=\sqrt{1.04}-1=0.019804

Model

Model

Price the coupon stream as c times a discounted geometric sum and add the discounted 250 redemption payment.

582.53=c∑k=112(1.02)kvk+250v12582.53=c\sum_{k=1}^{12}(1.02)^kv^k+250v^{12}

Compute

Compute

At j = 1.9804%, the coupon coefficient is 12.015 and redemption is worth 197.579. Solving gives c = 32.04.

582.53=12.015c+197.579⟹c=32.04582.53=12.015c+197.579\Longrightarrow c=32.04

Answer

Answer

The calculation gives 32.04 for geometrically increasing coupons, matching published choice A.

c=32.04(A)\boxed{c=32.04\quad\text{(A)}}