Independent solution

How to solve this Growing Annuity Present Value question

Setup

Setup

Payment t is 5,000(1.07)ᵗ and is discounted at 5%. The ratio of successive present-value terms is therefore 1.07/1.05.

PV=5000∑t=120(1.07)tvt,v=1/1.05PV=5000\sum_{t=1}^{20}(1.07)^tv^t,\quad v=1/1.05

Model

Model

Write the twenty discounted payments as a finite geometric series. Because the growth rate exceeds the discount rate, retaining the correct first term and twentieth endpoint is essential.

PV=50001.07v−(1.07v)211−1.07vPV=5000\frac{1.07v-(1.07v)^{21}}{1-1.07v}

Compute

Compute

Evaluating the series gives 122,617, which rounds to 122,600.

PV=122617PV=122617

Answer

Answer

The calculation gives 122,600 for growing annuity present value, matching published choice D.

PV=122600(D)\boxed{PV=122600\quad\text{(D)}}