Assuming that the gift cards have equal value the value of each will be is:$5, $5.
Gift Card 1 (C=GC1) has a value of $165 - Time×(-$4/30 days)
Lets set T for a time increment of 30 days
1 T = 30 days
Value of GC1, in increments of 30 days=GC1 = 165 - T×($4/30days)
Gift Card 2=GC2 = 145 - T×($3.50/30days)
Let find the value of T when the cards are equal in value
165-T×4 = 145 - T×3.50
where T= increments of 30 days
Re-arrange
=165-145=4-3.50
=20 = 0.5T
Divide both side by 0.5T
T-20/0.5
T = 40 days
Hence:
Value of each card
Card 1 after 40 periods=$165 - (40×$4)
Card 1 after 40 periods=$165-$160
Card 1 after 40 periods=$5
Card 2 after 40 periods= $145 - (40×3.5)
Card 2 after 40 periods = $5
Therefore assuming that the gift cards have equal value the value of each will be is:$5, $5.
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