Question

7.
Find the time for which $1,250.00 will amount to$ 2,031.25 at 12.5 % per annum
simple interest
A. 2 years
B 3 years
C4 years
D. 5 years

Answer 1

To determine the time required for an initial principal of $1,250.00 to amount to$2,031.25 at an annual simple interest rate of 12.5%, follow these steps:

1. Understand the Simple Interest Formula:
The formula to calculate the amount in simple interest is:
$\[ A = P + I \]$
where $\( A \)$ is the total amount, $\( P \)$ is the principal, and $\( I \)$ is the interest.

2. Interest Calculation:
Simple interest ($\( I \)$) can be calculated using:
$\[ I = P \times R \times T \]$
where $\( R \)$ is the rate per annum (expressed as a decimal) and $\( T \)$ is the time in years.

3. Combine Equations:
Combine the formulas to express the total amount $\( A \)$:
$\[ A = P + PRT \]$
$\[ 2031.25 = 1250 + 1250 \times 0.125 \times T \]$

4. Isolate $\( T \)$:
Rearrange the equation to solve for $\( T \)$:
$\[ 2031.25 = 1250(1 + 0.125T) \]$
$\[ 2031.25 = 1250 + 1250 \times 0.125T \]$
$\[ 2031.25 - 1250 = 1250 \times 0.125T \]$
$\[ 781.25 = 1250 \times 0.125T \]$
$\[ 781.25 = 156.25T \]$

5. Solve for $\( T \)$:
$\[ 781.25 = 156.25T \]$
$\[ T = \frac{781.25}{156.25} \]$
$\[ T = 5 \]$

Therefore, the time for which $1,250.00 will amount to$2,031.25 at an annual simple interest rate of 12.5% is 5 years.

The correct answer is:
D. 5 years