Question

Assume that you have a balance of $5000 on your mastercard and that you make no more charges. assume that mastercard charges 12% apr and that each month you make only the minimum payment of 5% of the balance. find a formula for the balance b after t monthly payments. (enter numerical values to four decimal places.) hint 1: you must write the formula as an equation, which means it should include an equal sign with variables and/or constants on both sides. the initial balance is entered in exact form. the product within the square brackets should be entered as a single number that is rounded to four decimal places. hint 2: you are not required to use the symbol palette that appears on screen. you may use your keyboard to type , =, and *(which is the keyboard version of the multiplication symbol). hint 3: type the ^ before the exponent or use the symbol palette to enter the exponent.

Answer 1

The formula for the balance after t monthly payments is b = (1 - 0.05)^t * 5000, where b is the balance and t is the number of monthly payments. This formula takes into account the minimum payment of 5% and the initial balance of $5000.

Step-by-step explanation:

To find a formula for the balance b after t monthly payments, we can use the following equation:

b = (1 - 0.05)t * 5000

Let's break down the equation:

• The term (1 - 0.05) represents the remaining balance after making the minimum payment of 5% each month. This term is raised to the power of t, the number of monthly payments made.
• Multiplying this term by the initial balance of $5000 gives us the balance after t monthly payments.

For example, if t=6:

b = (1 - 0.05)6 * 5000 = (0.95)6 * 5000 = 0.7351 * 5000 = 3675.50

After 6 monthly payments, the balance would be approximately $3675.50.