Question

determine whether the statement is true or false. if the statement is false, make the necessary change(s) to produce a true statement. if $6000 is borrowed at 9.2% for two months, the loans future value is $92. choose the correct answer below. a. the statement is true. b. the statement is false. if $6000 is borrowed at 9.2% for two months, the loans future value is $920. c. the statement is false. if $6000 is borrowed at 9.2% for one months, the loans future value is $92. d. the statement is false. if $6000 is borrowed at 9.2% for two months, the loans future value is $6092.

Explanation:

Step1: Recall Simple Interest Formula

The formula for simple interest is $I = P \times r \times t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. The future value $A$ is $A = P + I$.

Step2: Convert Time and Rate

Given $P = \$6000$, $r = 9.2\% = 0.092$ (annual rate), and $t = \frac{2}{12}$ years (since 2 months is $\frac{2}{12}$ of a year).

Step3: Calculate Interest

First, calculate the interest $I$:
$I = 6000 \times 0.092 \times \frac{2}{12}$
$I = 6000 \times 0.092 \times \frac{1}{6}$
$I = 1000 \times 0.092$
$I = \$92$

Step4: Calculate Future Value

Now, find the future value $A$:
$A = P + I = 6000 + 92 = \$6092$

Step5: Evaluate the Options

• Option A: False, since future value is $\$6092$, not $\$92$.
• Option B: False, future value is not $\$920$ (interest is $\$92$, so $A = 6092$).
• Option C: For 1 month, $t = \frac{1}{12}$, $I = 6000 \times 0.092 \times \frac{1}{12} = 46$, so future value would be $6046$, not $\$92$.
• Option D: Correct, as $A = 6000 + 92 = \$6092$.

Answer:

D. The statement is false. If $6000 is borrowed at 9.2% for two months, the loan’s future value is $6092.