3.3.7 Uniform Gradient Series Annual Equivalent Amount The objective of this mode of investment is to find the annual equivalent amount of a series with an amount Al at the end of the first year and with an equal increment (G) at the end of each of the following n - 1 years with an interest rate i compounded annually. The corresponding cash flow diagram is shown in Fig. 3.12. 0 1 2 3 4 10 Al A1+G A1+2G A1+3G A1+ (n - 1)G Fig. 3.12 Cash flow diagram of uniform gradient series annual equivalent amount. The formula to compute A under this situation is (1 + i)" - in - 1 A = Al + G i(1 + i)" - i = A1 + G (A/G, i, n) where (A/G, i, n) is called uniform gradient series factor. EXAMPLE 3.7 A person is planning for his retired life. He has 10 more years 36 Engineering Economics of service. He would like to deposit 20% of his salary, which is Rs. 4,000, at the end of the first year, and thereafter he wishes to deposit the amount with an annual increase of Rs. 500 for the next 9 years with an interest rate of 15%. Find the total amount at the end of the 10th year of the above series