Question

select the function that represents the simple interest formula. a. $a(n) = (n - 1)(p cdot n)^i$, where $n$ is any real number b. $a(n) = p(1 + i)^{n - 1}$, where $n$ is a positive integer c. $a(n) = p + (n - 1)i cdot p$, where $n$ is a positive integer d. $a(n) = n + (i - 1) cdot p$, where $n$ is a positive integer

Explanation:

Step1: Recall simple interest formula

The total amount $A$ after $n$ periods with principal $P$, periodic interest rate $i$ is $A = P + I$, where simple interest $I = P \cdot i \cdot t$, and $t$ is time in periods. For $n$ compounding periods (positive integer), $t = n-1$ (adjusting for period indexing).

Step2: Substitute interest into total amount

Substitute $I = P \cdot i \cdot (n-1)$ into $A = P + I$:
$A(n) = P + (n-1)i \cdot P$

Step3: Match to options

Compare with given choices; this matches option C. Option B is compound interest, others do not follow simple interest structure.

Answer:

C. $A(n) = P+ (n - 1)i\cdot P$, where $n$ is a positive integer