Question
Tavon has a $50 gift card that loses $2 for each 30 day period it is not used . He has $40 card that loses $1.50 for each 30 day period it is not used .
Write and solve an equation for the number of 30 day periods until the value of the gift cards will be equal ?
Hint:
Value after loosing value for not using = current value - single 30 days period × value lost per 30 day period.
The correct answer is: After 20 periods of 30 days each, the value of both the cards would be the same.
Step-by-step solution:-
Let a single 30 day period be x.
Now, we know that the gift card looses a certain value after a certain number of 30 days periods pass.
∴ for the $ 50 gift card-
Value after loosing value for not using = current value - single 30 days period × value lost per 30 day period
∴ Value after loosing value for not using = 50 - x × 2
∴ Value after loosing value for not using = 50 - 2x ......................................... (Equation i)
∴ for the $ 40 gift card-
Value after loosing value for not using = current value - single 30 days period × value lost per 30 day period
∴ Value after loosing value for not using = 40 - x × 1.5
∴ Value after loosing value for not using = 40 - 1.5x ......................................... (Equation ii)
Now, we need to find the value of x for which both the cards have equal value
∴ Value of $ 50 gift card = Value of $ 40 gift card
∴ 50 - 2x = 40 - 1.5x ................................... (From Equations i & ii)
∴ 50 - 40 = -1.5x + 2x ................................. (Taking all variables and constants on either side of the equation)
∴ 10 = 0.5x
∴ 
= x
∴ 20 = x
Final Answer:-
∴ After 20 periods of 30 days each, the value of both the cards would be the same.
The quantity of goods in general that will be exchanged for one unit of money is then the value of money. Money's value is defined as its purchasing power, or the amount of goods and services it can buy.
The time value of money (TVM) is the idea that a sum of money is worth more now than it will be at a later date because of the potential earnings in the interim. A sum of money in hand is more valuable than the same sum to be paid later. The time value of money is another name for the present discounted value.
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