Independent solution

How to solve this Annuities question

Setup

Setup

Solve the quarterly effective rate from the first perpetuity-due price.

300=1+jj300=\frac{1+j}{j}
j=1/299j=1/299

Model

Model

Convert sixteen quarterly periods to the effective four-year rate k.

1+k=(1+j)161+k=(1+j)^{16}

Compute

Compute

The four-year rate is 0.05487515. Solving 300 = X(1 + k)/k gives X = 15.606155.

300=X1+kk300=X\frac{1+k}{k}
X=15.60615535X=15.60615535

Answer

Answer

The four-year beginning payment is approximately 15.61, selecting choice B.

X≈15.61(B)\boxed{X\approx15.61\quad\text{(B)}}