You have a balance of $7500 on your credit card and you make no further charges. If
your APR is 12.5% and each month you make only the minimum payment of 5% of
your balance, then find a formula for the balance after
t
monthly payments.
A) 7500(0.959896)
t
B) 7500(0.940104)
t
C) 7500(1.03906)
t
D) 7500(1.06094)
t
D) 7500(1.06094)
t
To find the formula for the balance after t monthly payments, we need to consider the following information:
- The initial balance: $7500
- The APR: 12.5%
- The minimum monthly payment: 5% of the balance
The minimum payment formula can be written as follows:
Minimum Payment = 0.05 * Balance
To calculate the new balance after each monthly payment, we need to subtract the minimum payment from the previous balance and then add the accrued interest.
The formula for accrued interest can be written as follows:
Accrued Interest = Balance * (APR / 12)
To calculate the balance after t months, we need to repeat the process t times. Therefore, the formula for the balance after t months can be derived as:
Balance(t) = ((Balance - Minimum Payment) + (Balance * (APR / 12))) * ((1 + (APR / 12))^t)
Let's substitute the given values into the formula to find the correct answer option:
Balance(t) = ((7500 - (0.05 * 7500)) + (7500 * (0.125 / 12))) * ((1 + (0.125 / 12))^t)
Simplifying further, we get:
Balance(t) = (7500(0.95) + 781.25) * (1.01041667)^t
Calculating the values, we find that:
Balance(t) ≈ 7500(0.940104)^t
So the correct answer is option B:
7500(0.940104)^t