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Geometric Gradient Series

A geometric gradient changes by a constant percentage each period.

$$A_n=A(1+r)^{n-1}, \qquad W=\frac{1+r}{1+i}$$
$$P=\frac{A(1-W^n)}{(1+i)(1-W)}$$

Problem 45: Geometric Maintenance Cost

Annual maintenance is P1,500 for the first year and increases 10% every year. Find the present worth for 6 years at 8%.

$$W=\frac{1.10}{1.08}=1.0185$$
$$P=\frac{1500[1-(1.0185)^6]}{(1.08)(1-1.0185)}=8,728$$

Final answer: P8,728.

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