Given this formula to calculate a monthly mortgage payment: M = P * (i(1+i)^n) / ((1+i)^n - 1) and these declarations: double m; double i = 0.05/12; //monthly interest rate int p = 100_000…

Question

Options

• Am = p * (Math.pow(1 + r, n) / (Math.pow(1 + r, n) - 1));
• Bm = p * (r * Math.pow(1 + r, n) / (Math.pow(1 + r, n) - 1));
• Cm = p * (r * Math.pow(1 + r, n) / Math.pow(1 + r, n) - 1);
• Dm = p * (r * Math.pow(1 + r, n) / (Math.pow(1 + r, n) - 1));

• A
  78% (29)
• B
  3% (1)
• C
  14% (5)
• D
  5% (2)

Explanation

There is an error in this question's answer key. Option A is actually incorrect - it is missing the r * (interest rate) multiplication in the numerator, so it computes P * (1+i)^n / ((1+i)^n - 1) instead of the required formula. The correct code should be B or D, both of which faithfully translate M = P * [i(1+i)^n] / [(1+i)^n - 1].

Here is the breakdown of each choice:

• A - Wrong. Missing r * in the numerator entirely, so the interest rate i is dropped from the calculation.
• B - Correct implementation. Has r * Math.pow(1 + r, n) in the numerator and (Math.pow(1 + r, n) - 1) properly wrapped in parentheses for the denominator.
• C - Wrong parentheses around the denominator. Due to operator precedence, / binds before -, so it computes (r * (1+r)^n / (1+r)^n) - 1, which simplifies incorrectly to r - 1.
• D - Appears identical to B and is also a correct implementation (the question may have a typo distinguishing B from D).

Memory tip: The denominator (1+i)^n - 1 must be wrapped in its own parentheses - the entire expression subtracts 1 from the power, so without those parens Java's division operator will steal the subtraction first and break the formula.

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