Grep has a credit card which requires a minimum monthly payment of 2.00% of the total balance or $11.45. Consumption monthly is represented in the table below:
| Month | Cost ($) |
|---|---|
| Jan | 600 |
| Feb | 335 |
| Mar | 269.8 |
| Apr | 97.24 |
| May | 112.51 |
| Jun | 72.4 |
| Jul | 41.14 |
| Aug | 101.54 |
Grep makes only the minimum monthly payment in May, June, and July. What will his total balance be after he makes the monthly payment for July? (Assume that interest is compounded before the monthly payment is made, and that the monthly payment is made at the end of the month. Round all dollar values to the nearest cent.)
Answer (1)
Calculate the balance after March: B a l an c e M a rc h = 4600 + 335 = 4935 .
Calculate the balance after May: B a l an c e M a y = 7633 − ( 0.02 × 7633 ) = 7480.34 .
Calculate the balance after June: B a l an c e J u n e = 7577.58 − ( 0.02 × 7577.58 ) = 7426.03 .
Calculate the balance after July: B a l an c e J u l y = 7538.54 − ( 0.02 × 7538.54 ) = 7387.77 . The final balance is $7387.77 .
Explanation
Understanding the Problem We are given a credit card balance problem where Greg makes minimum monthly payments. We need to calculate his total balance after the July payment, assuming interest is compounded monthly before the payment, and all dollar values are rounded to the nearest cent. The minimum monthly payment is 2% of the total balance. We will assume an interest rate of 0% since it is not provided.
Balance After March First, we calculate the balance after March by adding the March cost to the initial balance: B a l an c e M a rc h = 4600 + 335 = 4935
Balance After April Next, we calculate the balance after April. Since no payment or cost is given for April, assume no change in balance: B a l an c e A p r i l = B a l an c e M a rc h = 4935
Balance After May Now, we calculate the balance after May. First, we add the May cost to the balance: B a l an c e M a y , b e f ore P a y m e n t = B a l an c e A p r i l + 2698 = 4935 + 2698 = 7633 Then, we calculate the minimum payment for May: P a y m e n t M a y = 0.02 × B a l an c e M a y , b e f ore P a y m e n t = 0.02 × 7633 = 152.66 Finally, we subtract the payment: B a l an c e M a y = B a l an c e M a y , b e f ore P a y m e n t − P a y m e n t M a y = 7633 − 152.66 = 7480.34
Balance After June We calculate the balance after June. First, we add the June cost to the balance: B a l an c e J u n e , b e f ore P a y m e n t = B a l an c e M a y + 97.24 = 7480.34 + 97.24 = 7577.58 Then, we calculate the minimum payment for June: P a y m e n t J u n e = 0.02 × B a l an c e J u n e , b e f ore P a y m e n t = 0.02 × 7577.58 = 151.55 Finally, we subtract the payment: B a l an c e J u n e = B a l an c e J u n e , b e f ore P a y m e n t − P a y m e n t J u n e = 7577.58 − 151.55 = 7426.03
Balance After July We calculate the balance after July. First, we add the July cost to the balance: B a l an c e J u l y , b e f ore P a y m e n t = B a l an c e J u n e + 112.51 = 7426.03 + 112.51 = 7538.54 Then, we calculate the minimum payment for July: P a y m e n t J u l y = 0.02 × B a l an c e J u l y , b e f ore P a y m e n t = 0.02 × 7538.54 = 150.77 Finally, we subtract the payment: B a l an c e J u l y = B a l an c e J u l y , b e f ore P a y m e n t − P a y m e n t J u l y = 7538.54 − 150.77 = 7387.77
Final Answer Therefore, the total balance after the July payment is $7387.77 .
Examples
Credit card balances and payments are a common real-world application of arithmetic sequences and percentages. Understanding how minimum payments, interest rates, and additional charges affect your balance is crucial for managing personal finances. This problem demonstrates how to calculate the balance after several months, considering minimum payments and additional costs. This type of calculation can help individuals make informed decisions about their spending and repayment strategies, ultimately leading to better financial health.
