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This year, I place 100 dollars into an account with a zero…

This year, I place...

This year, I place 100 dollars into an account with a zero dollar balance, and plan to continue on contributing annually for n amount of time.Part (A)
Every two years, I increase the amount I place in by $100. In the first 8 years (n=8) my contribution schedule looks like this:###-##-####200 300 300 400 400Please construct a formula for the balance/future value/total amount (y) in year (n). Please show your work and explain the variables and operations used to construct the formula in step by step order.Part (B)
Every two years, instead of increasing the mount by $100, I double the amount I contribute. In the first 8 years (n=8) my contribution schedule looks like this:
100 100 200 200 400 400 800 800Please construct a formula for the balance/future value/total amount (y) in year (n). Please show your work and explain the variables and operations used to construct the formula in step by step order. Hi Pearl I'm looking for help on the question above

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Answered in 51 minutes by:
3/28/2018
Brad Summers
Category: Math Homework
Satisfied Customers: 57
Experience: Mathematics Teacher at Baldivis Secondary College
Verified

Hi,

A)

Remember that the sum from 1 to n is n(n+1)/2

Then for part A:

If n is even formula is: 100*2(n/2)(n/2+1)/2 = 100(n/2)(n/2+1)

If n is odd formula is 100*2((n-1)/2)((n-1)/2+1)/2 + (n+1)50

B)

Remember that the sum from0 to n of 2n is 2exp(n+1)-1

Then for part B:

If n is even formula is:100*2*(2exp((n-2)/2+1)-1) = 200(2exp(n/2)-1)

If n is odd formula is100*2(2exp((n-3)/2+1)-1) + 100*2exp((n-1)/2)

Tell me if you need more details

Thanks

Brad

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Customer reply replied 3 months ago
Hi Brad, appreciate yout response. There are two things which are still not clear that I need help resolving. First, how do we get to here "Remember that the sum from 1 to n is n(n+1)/2", and, second, how are you getting to the formulas, for both Part A and Part B, and can we not develop a single formula for calculating the year without the preface of odd or even?I'm unsure if possible but insight here would finish the question. Appreciate very much your help in wrapping out the answer.

Ok

In part A) we used the Formula for the sum of the first integers from 1 to n is n(n+1)/2 (Gauss sum) is a classic result, ido not think you need to justify that

In part B) we used the geometric sum: 1+2+2exp(2) +2exp(3) +....2exp(n) is a result of series

Than sum is 2exp(n+1) -1

About your second question, yes we can construct a formula

without even and odd , but will be more complex

You have to know functons like floor(x)

Tell me if you need that or is enough

Thanks

Brad Summers
Category: Math Homework
Satisfied Customers: 57
Experience: Mathematics Teacher at Baldivis Secondary College
Verified
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