Comparing Payment Plans: Calculating Months Needed

[nickenrite]

sequences help!

If possible could you show working and eqn^s used thanks.

'moe plans to set up his own painting company so he has been looking for a tidy, recent model, second hand van to transport his equipment to jobs. He sees one that that will be perfect and notes that there are two possible payment regimes.

Plan A: pay a deposit of$4950
first month pay $300
each successive month pay $20 more than the previous month.

PlanB:pay a deposit $7995
first month pay $61each successive month pay $10 less than the previous month.

Calculate how many months it will take before the total paid into planA would be the same amount paid into planB.


thanks for your time

 

[courtrigrad]

Plan A: $$P_{1} = 4950+(300 + 20(n-1))$$

Plan B: $$P_{2} = 7995 + (61-10(n-1))$$

$$n = 1$$ corresponds to the first month.

Now set $$P_{1}=P_{2}$$ , and solve for $$n$$