Question

You owe $300 on your credit card. For every month that you fail to make a payment, your balance increases by 3%. Find a formula for the balance

b owed after t months with no payment.

a.b=300×(1+0.03)t
b.b=300×(0.03)t
c.b=300×(1−0.03)t
d.b=300×(1.03)t

Answer 1

The formula for the balance owed after t months with no payment is b = 300 × (1.03)^t, which uses the principle of compound interest to calculate the new balance including the monthly increase of 3%.

Step-by-step explanation:

When you owe $300 on your credit card, and the balance increases by 3% every month due to non-payment, we need to find a formula that calculates the new balance after a certain number of months, t. the balance increases by a factor of 1.03 each month, where this factor represents the original amount plus the 3% increase. therefore, the formula to find the balance b after t months of non-payment is option d.

b = 300 × (1.03)^t

This formula uses the principle of compound interest, where the new balance is the previous balance multiplied by the growth rate (1 + the interest rate). the formula is derived by taking the original balance and multiplying it by the growth factor raised to the power of the number of periods of growth, in this case, months of non-payment.