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Answer :
The correct sequence showing the increasing balance is Option D: 650.00, 661.70, 673.61, 685.74, 698.08, and so on.
The sequence that describes Miriam's increasing monthly balance due to compound interest needs to reflect the compounding effect of the 1.8% interest rate applied each month. With a starting balance of $650, after one month with the interest rate of 1.8%, the new balance would be $650 * (1 + 0.018) = $650 * 1.018 = $661.70.
To find the subsequent months' balances, we continue to multiply the previous balance by 1.018 (which is 1 + 1.8%). For example, the balance after the second month would be $661.70 imes 1.018 = $673.61, and so on. This process is known as geometric progression where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio (in this case, 1.018).
Thus, the correct sequence that represents Miriam's increasing debt is Option D: 650.00, 661.70, 673.61, 685.74, 698.08, and so on.
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