Arith., Geo. Series: You are to receive a monthly stipend

[guitarkid583]

You are to receive a monthly stipend from your relative over a 4 year period of time. Pick the method that will result in the most amount of money.

Method A: The first month you will recieve $250, and every month after that you will recieve $250 more than the month before.

Method B: Each month the monthly stipend is 20% larger than the previous months, with the first monthly stipend being set at $20.00.

Can someone please show me with work how to solve this?

Thanks

 

[skeeter]

method A ...

250 + 2(250) + 3(250) + ... + 48(250) =

250(1 + 2 + 3 + ... + 48) = ?



method B ...

250 + 250(1.2) + 250(1.2)² + 250(1.2)³ + ... + 250(1.2)⁴⁷ =

250[(1.2)⁰ + (1.2)¹ + (1.2)² + (1.2)³ + ... + (1.2)⁴⁷] = ?

 

[Denis]

In case you need to show formulas:

Case #1:
f = first month's, n = number of months:

formula: f[n(n+1)/2)]

250[48(49)/2)] = $294,000

Case #2:
m = monthly amount, i = monthly % increase, n = number of months:

formula: m[(1 + i)^n - 1] / i

20[(1 + .2)^48 - 1] / .2 = ~$631,875 : wish I had such a relative :wink: