A fully amortizing loan has a principal balance of $100,000 immediately before a $900 principal-and-interest payment. If $500 of the payment is interest, what is the new principal balance?
Correct Answer
D) $99,600
Why this is correct: The payment amount is $900. Of this, $500 is allocated to interest. The remainder is applied to principal. Calculate the principal portion: $900 total payment - $500 interest = $400 principal reduction. The starting balance is $100,000. Subtract the principal reduction to find the new balance: $100,000 - $400 = $99,600. Why the other choices are wrong: The choice "$99,100" is incorrect; it results from subtracting the full payment from the balance ($100,000 - $900). The choice "$99,500" is incorrect; it results from subtracting only the interest portion from the balance ($100,000 - $500). The choice "$100,400" is incorrect; it results from adding the principal portion to the balance instead of subtracting it. Exam tip: In balance calculations, remember the formula: New Balance = Old Balance - (Total Payment - Interest Portion). Always isolate the principal reduction first.
Why This Is the Correct Answer
Why this is correct: The payment amount is $900. Of this, $500 is allocated to interest. The remainder is applied to principal. Calculate the principal portion: $900 total payment - $500 interest = $400 principal reduction. The starting balance is $100,000. Subtract the principal reduction to find the new balance: $100,000 - $400 = $99,600. Why the other choices are wrong: The choice "$99,100" is incorrect; it results from subtracting the full payment from the balance ($100,000 - $900). The choice "$99,500" is incorrect; it results from subtracting only the interest portion from the balance ($100,000 - $500). The choice "$100,400" is incorrect; it results from adding the principal portion to the balance instead of subtracting it. Exam tip: In balance calculations, remember the formula: New Balance = Old Balance - (Total Payment - Interest Portion). Always isolate the principal reduction first.
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