With the equation F=P*(1+i)^n

Question

BlackTom AI · Accepted Answer

The compound-interest formula F = P(1 + i)^n defines i as the interest rate per period and n as the number of those periods, so consistency of units, proper numeric form for i, and the i = 0 special case follow directly.

1) n and i must be stated in the same time units: i is the rate per period and n counts periods. If i is an annual rate and n is in years, they match and you may apply the formula directly. If n is in months while i is annual you must convert one to the other. Example: annual i = 0.05. Monthly i_month = (1 + 0.05)^(1/12) − 1 ≈ 0.004074. For 24 months, use F = P(1 + 0.004074)^{24} — not F = P(1 + 0.05)^{24}.

2) F = P if i = 0: substitute i = 0 into the formula: F = P(1 + 0)^n = P(1)^n = P. This is an immediate algebraic result: with zero interest there is no change in value over time.

3) i must be stated as a decimal, not a percentage: the formula uses numeric multiplication by (1 + i). A 6% rate corresponds to i = 0.06. If P = 100 and n = 2, correct use gives F = 100(1 + 0.06)^2 = 100(1.1236) = 112.36. If you mistakenly used i = 6 (i.e., treated percent as 6), you'd compute F = 100(7)^2 = 4900, which is clearly wrong.

Each of the three individual statements is therefore correct, so the correct choice is: All of these are correct. This matches the provided answer.

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