You set a goal to save at least 1,100 over a six week period. You are trying to decide between two plans. You are trying to decide between two plans
Plan A: Deposit $100 the first week and deposit 25% more each successive week for the next 5 weeks
Plan B: Deposit $125 the first week and deposit 15% more each successive week for the next 5 weeks
which plan will result in total savings of at least $1,100? I would appreciate an explanation and showing your work.
Assuming no interest rates are involved,
PLanA : 100 + 100(1.25) + 100(1.25)^2 + ...
Plan B: 125 + 125(1.15) + 125(1.25)^2 + ..
each one is a GS,
first one: a = 100, r = 1.25, n = 6
2nd one: a = 125, r = 1.15, n = 6
I will find the sum of the 2nd plan, you find the sum of the first
sum(n) = a(r^n - 1)/(r-1)
= 125(1.15^6 - 1)/(1.15-1)
= 125(1.011357)/.15 = 1094.21
I have found the answer to be plan A? is this correct
yes
To determine which plan will result in total savings of at least $1,100, we can calculate the savings for each week and then add them up to find the total savings for both plans. Let's calculate the savings for each plan.
Plan A:
- Week 1: Deposit $100.
- Week 2: Deposit 25% more than the previous week. So, $100 + 25% of $100 = $100 + $25 = $125.
- Week 3: Deposit 25% more than the previous week. So, $125 + 25% of $125 = $125 + $31.25 = $156.25.
- Week 4: Deposit 25% more than the previous week. So, $156.25 + 25% of $156.25 = $156.25 + $39.06 = $195.31.
- Week 5: Deposit 25% more than the previous week. So, $195.31 + 25% of $195.31 = $195.31 + $48.83 = $244.14.
- Week 6: Deposit 25% more than the previous week. So, $244.14 + 25% of $244.14 = $244.14 + $61.04 = $305.18.
Plan B:
- Week 1: Deposit $125.
- Week 2: Deposit 15% more than the previous week. So, $125 + 15% of $125 = $125 + $18.75 = $143.75.
- Week 3: Deposit 15% more than the previous week. So, $143.75 + 15% of $143.75 = $143.75 + $21.56 = $165.31.
- Week 4: Deposit 15% more than the previous week. So, $165.31 + 15% of $165.31 = $165.31 + $24.80 = $190.11.
- Week 5: Deposit 15% more than the previous week. So, $190.11 + 15% of $190.11 = $190.11 + $28.52 = $218.63.
- Week 6: Deposit 15% more than the previous week. So, $218.63 + 15% of $218.63 = $218.63 + $32.79 = $251.42.
Now, let's calculate the total savings for each plan.
Plan A: $100 + $125 + $156.25 + $195.31 + $244.14 + $305.18 = $1,126.88
Plan B: $125 + $143.75 + $165.31 + $190.11 + $218.63 + $251.42 = $1,094.22
Therefore, Plan A will result in a total savings of at least $1,100, while Plan B will not.