Middle School

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Many credit card companies charge a compound interest rate of 1.8% per month on a credit card balance. Miriam owes $650 on a credit card. if she makes no purchases or payments, she will go more and more in debt.
Which of the following sequences describes her increasing monthly balance?​

Many credit card companies charge a compound interest rate of 1 8 per month on a credit card balance Miriam owes 650 on a credit

Answer :

Answer:

The correct answer is D. 650.oo, 661.70, 673.61, 685.74, 698.08

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Compound interest rate charged by Miriam's credit card company = 1.8% monthly

2. If she makes no purchases or payments, she will go more and more in debt. Which of the following sequences describes her increasing monthly balance?​

Miriam's current credit card balance = US$ 650

Miriam's credit card balance in one month = 650 * 1.018

Miriam's credit card balance in one month = 661.70

Miriam's credit card balance in two months = 661.70 * 1.018

Miriam's credit card balance in two months = 673.61

Miriam's credit card balance in three months = 673.61 * 1.018

Miriam's credit card balance in three months = 685.74

Miriam's credit card balance in four months = 685.74 * 1.018

Miriam's credit card balance in four months = 698.08

The correct answer is D. 650.oo, 661.70, 673.61, 685.74, 698.08

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Rewritten by : Barada

Final answer:

Miriam's increasing credit card balance due to compounding monthly interest can be calculated using the formula for compound interest, P(1 + r)ⁿ. By applying the 1.8% interest rate each month, her balance will increase from an initial $650 to greater values, with each month's balance serving as the base for the next month's interest calculation.

Explanation:

The question involves finding a sequence that describes Miriam's increasing monthly balance on her credit card. Since the credit card company is charging a compound interest rate of 1.8% per month, and Miriam currently owes $650, we need to calculate her new balance each month by applying this interest rate.

To calculate the balance for each subsequent month, we can use the formula for compound interest, which is P(1 + r)ⁿ, where P is the principal amount (initial balance), r is the monthly interest rate as a decimal, and n is the number of months.

For the first month, her new balance would be $650 × (1 + 0.018) = $661.70.

For the second month, we use the new balance as the principal and apply the formula again: $661.70 × (1 + 0.018) = $673.70.

This process is repeated each month to find the increasing balance. Therefore, the sequence describing her increasing monthly balance will show gradual increments as the interest compounds month-over-month.