The formulas used in this comparison are as follows:
Total Cost (Buying Phone Outright):
\[ \text{Total Cost} = \text{Retail Price} + \text{Own Phone Monthly Payment} \times \text{Contract Length} \]
Total Cost (Carrier Plan):
\[ \text{Total Cost} = \text{Carrier Monthly Payment} \times \text{Contract Length} - \text{Interest Generated} \]
Where Interest Generated is calculated as:
\[ \text{Interest Generated} = \text{Retail Price} \times \left(1 + \frac{\text{Interest Rate}}{12}\right)^{\text{Contract Length}} - \text{Retail Price} \]
This calculator helps you compare the total costs of two cell phone plans: one where you buy the phone outright and one where you get the phone on a carrier plan. By considering the retail price of the phone, contract length, monthly payments, and interest rate, you can determine which option is more economical in the long run.
Let's assume the following for a cell phone plan comparison:
Step 1: Calculate total cost if buying the phone outright:
\[ \text{Total Cost} = 800 + 20 \times 24 = 1,280 \]
Step 2: Calculate the monthly difference:
\[ \text{Monthly Difference} = 50 - 20 = 30 \]
Step 3: Calculate the interest generated on the savings account:
\[ \text{Interest Generated} = 800 \times \left(1 + \frac{4}{12}\right)^{24} - 800 = 35.73 \]
Step 4: Calculate total cost if using the carrier plan:
\[ \text{Total Cost} = 50 \times 24 - 35.73 = 1,164.27 \]
In this case, the carrier plan is cheaper by $115.73.
