Select the correct answer.
Given the following formula, with $A=27$ and $t=3$, solve for $r$.
$A=P(1+r t)$
A. $r=\frac{27-1}{3 P}$
B. $r=\frac{27-P}{3}$
C. $r=\frac{26}{3}$
D. $r=\frac{27-P}{3 P}$
Answer (1)
Substitute given values into the formula.
Divide both sides of the equation by P : P 27 = 1 + 3 r .
Isolate r by subtracting 1 and then dividing by 3: r = 3 P 27 − P .
The correct answer is: r = 3 P 27 − P
Explanation
Understanding the Problem We are given the formula A = P ( 1 + r t ) , with A = 27 and t = 3 . We need to solve for r .
Substituting Values Substitute the given values of A and t into the formula: 27 = P ( 1 + 3 r ) .
Dividing by P Divide both sides by P : P 27 = 1 + 3 r .
Subtracting 1 Subtract 1 from both sides: P 27 − 1 = 3 r .
Finding Common Denominator Rewrite the left side with a common denominator: P 27 − P = 3 r .
Isolating r Divide both sides by 3: r = 3 P 27 − P .
Final Answer Therefore, the correct answer is D. r = 3 P 27 − P .
Examples
This formula is used in finance to calculate the future value of an investment with simple interest. For example, if you invest a principal amount P at a simple interest rate r for t years, the accumulated amount A can be calculated using this formula. Understanding how to solve for r allows you to determine the interest rate needed to reach a specific future value, which is crucial for financial planning and investment decisions. For instance, if you want to have 27 a f t er 3 ye a rs f ro m p r in c i p a l am o u n t P , yo u c an c a l c u l a t ere q u i re d in t eres t r a t e r$.
