What is the Average Income over Multiple Interest Days?

[Stclements]

I have various income flows
1000 for 173 days
9000 for 153 days
20000 for 123 days
30000 for 62 days
30000 for 31 days

what I am hoping to achieve is to find the average value over the given period, that period being 173 days

 

[Sudharaka]

I have various income flows
1000 for 173 days
9000 for 153 days
20000 for 123 days
30000 for 62 days
30000 for 31 days

what I am hoping to achieve is to find the average value over the given period, that period being 173 days

Hi Stclements, :)

Welcome to MHB! Just to clarify, does all these income occurs in the period of 173 days? That is over the entire period you get 1000 dollars, over a period of 153 days which is in the above 173 days you get an income of 9000, over a period of 123 days which is in the above 173 days you get 20000 and so on.

 

[Stclements]

That is correct 173 days is the total time period

 

[Sudharaka]

That is correct 173 days is the total time period

Then the average amount of money you receive in the 173 time period is the total amount of money in that period divided by 173. Hope you can continue. :)

 

[Stclements]

Surely if some sums of money have been in there longer than others simply dividing all the monies by all the days would not give an accurate representation of the overall average!

 

[AbrahamA]

Using number of days as weights, the weighted average would be more appropriate of a measure

I get 12,546.13 as the weighted average amount

 

[Stclements]

How did you calculate that number, for my benefit please.

 

[AbrahamA]

Depending on the scale of weights you could have used the answer should be the same

[ 1000 x 173 + 9000 x 153 + 20000 x 123 + 30000 x 62 + 30000 x 31 ] / [ 173 + 153 + 123 + 62 + 31 ]

[ 173000 + 1377000 + 2460000 + 1860000 + 930000 ] / 542

6800000 / 542

12,546.13

You could have scaled the weights by selecting the largest period as 1 and the intermediate periods as its fraction

I hope that would produce the same result

 

[Stclements]

Much appreciated.