Question

You start with $1000 and every day you will receive the previous day’s total plus an additional $1000 a day for 30 days. How much money will you have after 30 days?

Answer 1

The total earned after 30 days is 465000.

Explanation:

The amount of money that I'll recieve can be modelled as a arithmetic sequence in which the next element is related to the prior by a sum of a rate "q". This sequence can be seen below:

{1000, 2000, 3000, ...}

Where q = 1000. In order sum all the "n" terms on a sequence of this kind we can use the following formula:

Sn = (n/2)*(a1 + an)

And to find the term an, we can use the formula:

an = a0 + (n-1)*r

Where n is the position of the number we want to calculate, in this case 30, a0 is the first number on the sequence and r is the rate between consecutive numbers. So the 30th term is:

a30 = 1000 + (30 -1)*1000

a30 = 1000 + 29*1000

a30 = 1000 + 29000 = 30000

And the total obtained is:

s30 = (30/2)*(1000 + 30000) = (30/2)*(31000)

s30 = 930000/2 = 465000

The total earned after 30 days is 465000.