present value (p) can be computed using:\np=f(1+i)^n\np=f(1+i)^-n\nf=p+i\nf=p(1 - r)^n
present value (p) can be computed using:\np=f(1+i)^n\np=f(1+i)^-n\nf=p+i\nf=p(1 - r)^n
Answer
Explanation:
Step1: Recall present - value formula
The present - value formula for a future amount $F$ with an interest rate $i$ compounded for $n$ periods is $P = F(1 + i)^{-n}$. This formula is derived from the future - value formula $F=P(1 + i)^{n}$, and by solving for $P$, we get $P = F(1 + i)^{-n}$.
Step2: Analyze other formulas
The formula $P = F(1 + i)^{n}$ is incorrect as it is the future - value formula in the wrong form. The formula $F=P + I$ is the simple interest formula where $I$ is the interest amount. The formula $F = P(1 - r)^{n}$ is used for depreciation or decay scenarios, not for present - value calculation.
Answer:
$P=F(1 + i)^{-n}$ (the second option)