The simple interest formula is given by A(n) = P(1 + i*n), where:
- A(n) is the total amount after n periods,
- P is the principal amount,
- i is the rate of interest per period,
- n is the number of periods.
Now, let's examine each option:
A. A(n) = (n-1)(P * i)ⁿ:
This formula is not the representation of a simple interest formula as it includes n in the power, which differs significantly from the original formula.
B. A(n) = n + (P - 1)i * P:
This formula also does not represent the simple interest formula. The term (P - 1)i*P is unrelated to the simple interest formula, and there is no mathematical reason to add n to it.
C. A(n) = P(1 + i)ⁿ⁻¹:
Again, this formula does not mirror the simple interest formula. Even while structurally it may look somewhat similar, it contains an exponent of (n-1), which doesn't exist in the simple interest formula.
D. A(n) = P + (n - 1)i * P:
This equation is also not the representation of the simple interest formula. The term (n-1)i*P does not match the term i*n in the original equation.
I'm afraid none of the options listed is a correct representation of the simple interest formula. Additional information or criteria is required to answer this question. It appears there may have been an error in the formulation of the answers. It would be wise to check them again.