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In the future value formula for simple interest, [tex]A = P(1 + rt)[/tex], solve for the variable [tex]P[/tex].

Note: In this formula, [tex]A[/tex] represents future value, [tex]P[/tex] is present value (or principal), [tex]r[/tex] is rate, and [tex]t[/tex] is time.

A. [tex]P = \frac{A}{1 + rt}[/tex]
B. [tex]P = \frac{A}{rt}[/tex]
C. [tex]P = A(1 + rt)[/tex]
D. [tex]P = \frac{A}{1 + r}[/tex]


Sagot :

Let's solve for the variable [tex]\( P \)[/tex] in the future value formula for simple interest given by [tex]\( A = P(1 + r t) \)[/tex]. Here, [tex]\( A \)[/tex] represents the future value, [tex]\( P \)[/tex] is the present value (or principal), [tex]\( r \)[/tex] is the interest rate, and [tex]\( t \)[/tex] is time.

To isolate [tex]\( P \)[/tex], follow these steps:

1. Start with the given formula:
[tex]\[ A = P(1 + r t) \][/tex]

2. To solve for [tex]\( P \)[/tex], we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by [tex]\( (1 + r t) \)[/tex]:
[tex]\[ \frac{A}{1 + r t} = P \][/tex]

3. Rearrange the equation to express [tex]\( P \)[/tex] as the subject:
[tex]\[ P = \frac{A}{1 + r t} \][/tex]

Hence, the correct formula for [tex]\( P \)[/tex] is:
[tex]\[ P = \frac{A}{1 + r t} \][/tex]

This result indicates that to find the present value [tex]\( P \)[/tex], you need to divide the future value [tex]\( A \)[/tex] by the term [tex]\( (1 + r t) \)[/tex], which accounts for the interest rate and the time period.

Among the provided options, the correct one is:
[tex]\[ P = \frac{A}{1 + r t} \][/tex]