Interest formulas for Uniform gradient series

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Welcome to the lecture on the interest formula for uniform gradient series. So we've already discussed the single payment series and equal annual payment series. Now, this is a series where there is a gradient, but this gradient is linear. So, this is a non-uniform gradient series and a linear gradient series. In this series,

basically, the end-of-year payment is increasing by a linear mean in the first year. And if you pay ∑ in the second year, and f1 will be increased by a constant value, that is, suppose g. So, this g is the gradient. This g is uniform every year. So, in the second year, if it is f1 ∑

in the third year, it becomes f1 ∑ 2g. And so on. So, in the eighth year, and we're basically paying f1 ∑ n-1 nj. Now, in this case, we have to find what is the equivalent annual series. So, m is to find the equivalent annual end-of-year payment. For the gradient amount paid every year and so we can see by

referring to the table about the gradient series as we know the cash flow diagrams for such series is like this we have 0 1 2 th

for a minus v and a now in this s we have since we pay av during the first year and and this increases to av plus ggi in the second year so this is av and av plus ggi so this g is basically the gradient and this gradient will go on increasing so in the third year this amount will be av ≥