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
