Suppose Olivia has $$6,840$ in credit card debt on the VB credit card which has annual interest rate of $18\mathrm{.}2\%.$ Olivia is considering transferring her debt to the LA credit card that offers $0\%$ interest for $18$ months.

$($a$)$

If Olivia makes a payment of $$380$ per month on the VB credit card, what will her balance be at the end of $18$ months? Assume that no additional charges are made to the card. $($Suggestion: You are trying to find the future value of a debt that has a present value of $$6,840.$ Use the formula for the future value of an ordinary annuity. Round your answer to the nearest cent.$)$

$

$($b$)$

If Olivia makes a payment of $$380$ per month on the LA credit card, what will her balance be at the end of $18$ months? Assume that no additional charges are made to the card. $($Suggestion: None of the payment goes to interest on the debt. Round your answer to the nearest cent.$)$$

$0$

$($c$)$

How much lower is the balance due after $18$ months on the LA credit card? Note: Some credit card companies may charge a transfer fee which will affect the benefit of a $0\%$ introductory rate. Assume that there is not a transfer fee. $($Round your answer to the nearest cent.$)$

$