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Arithmetic Gradient Series

An arithmetic gradient changes by a constant amount each period.

$$A_{equiv}=G(A/G,i,n)$$

Problem 42: CE Board May 2022

Maintenance is $155 at the end of year 1 and increases by $35 each year for 8 years. Find the present worth at 6%.

$$P_1=155(P/A,6\%,8)=155(6.2098)=962.50$$
$$P_2=35(P/G,6\%,8)=35(19.845)=694.58$$

Final answer: $P=P_1+P_2=1,657$.

Problem 44: Retirement Gradient

Withdrawals start at $5,000 and increase by $1,000 yearly for 15 years. At 6%, find required savings at retirement.

$$A_2=1000(A/G,6\%,15)=1000(5.9260)=5,926$$
$$A_3=5000+5926=10,926$$
$$P=10926(P/A,6\%,15)=106,116.59$$

Final answer: $106,116.59.

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