Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To determine the time for which [tex]$1250.00 will accumulate to $[/tex]2031.25 at an annual simple interest rate of 12.5%, we can follow these steps:
1. Identify the given values:
- Principal ([tex]\(P\)[/tex]) = [tex]$1250.00 - Final Amount (\(A\)) = $[/tex]2031.25
- Annual Interest Rate ([tex]\(R\)[/tex]) = 12.5%
2. Understand the formula for simple interest:
The amount ([tex]\(A\)[/tex]) after time ([tex]\(T\)[/tex]) years can be calculated using the formula:
[tex]\[ A = P + PRT \][/tex]
which can be rearranged to:
[tex]\[ A = P(1 + RT) \][/tex]
3. Rearrange to solve for [tex]\(T\)[/tex]:
Starting from:
[tex]\[ A = P(1 + RT) \][/tex]
Isolating [tex]\(T\)[/tex], we get:
[tex]\[ 1 + RT = \frac{A}{P} \][/tex]
[tex]\[ RT = \frac{A}{P} - 1 \][/tex]
[tex]\[ T = \frac{\frac{A}{P} - 1}{R} \][/tex]
4. Substitute the known values into the equation:
- [tex]\(A = 2031.25\)[/tex]
- [tex]\(P = 1250.00\)[/tex]
- [tex]\(R = \frac{12.5}{100} = 0.125\)[/tex]
[tex]\[ T = \frac{\frac{2031.25}{1250.00} - 1}{0.125} \][/tex]
5. Perform the division and subtraction inside the fraction:
[tex]\[ \frac{2031.25}{1250.00} = 1.625 \][/tex]
[tex]\[ T = \frac{1.625 - 1}{0.125} \][/tex]
[tex]\[ T = \frac{0.625}{0.125} \][/tex]
6. Complete the division to find [tex]\(T\)[/tex]:
[tex]\[ T = 5 \][/tex]
Hence, the time for which [tex]$1250.00 will amount to $[/tex]2031.25 at a 12.5% per annum simple interest rate is [tex]\( \boxed{5} \)[/tex] years. Therefore, the correct answer is:
D. 5 years
1. Identify the given values:
- Principal ([tex]\(P\)[/tex]) = [tex]$1250.00 - Final Amount (\(A\)) = $[/tex]2031.25
- Annual Interest Rate ([tex]\(R\)[/tex]) = 12.5%
2. Understand the formula for simple interest:
The amount ([tex]\(A\)[/tex]) after time ([tex]\(T\)[/tex]) years can be calculated using the formula:
[tex]\[ A = P + PRT \][/tex]
which can be rearranged to:
[tex]\[ A = P(1 + RT) \][/tex]
3. Rearrange to solve for [tex]\(T\)[/tex]:
Starting from:
[tex]\[ A = P(1 + RT) \][/tex]
Isolating [tex]\(T\)[/tex], we get:
[tex]\[ 1 + RT = \frac{A}{P} \][/tex]
[tex]\[ RT = \frac{A}{P} - 1 \][/tex]
[tex]\[ T = \frac{\frac{A}{P} - 1}{R} \][/tex]
4. Substitute the known values into the equation:
- [tex]\(A = 2031.25\)[/tex]
- [tex]\(P = 1250.00\)[/tex]
- [tex]\(R = \frac{12.5}{100} = 0.125\)[/tex]
[tex]\[ T = \frac{\frac{2031.25}{1250.00} - 1}{0.125} \][/tex]
5. Perform the division and subtraction inside the fraction:
[tex]\[ \frac{2031.25}{1250.00} = 1.625 \][/tex]
[tex]\[ T = \frac{1.625 - 1}{0.125} \][/tex]
[tex]\[ T = \frac{0.625}{0.125} \][/tex]
6. Complete the division to find [tex]\(T\)[/tex]:
[tex]\[ T = 5 \][/tex]
Hence, the time for which [tex]$1250.00 will amount to $[/tex]2031.25 at a 12.5% per annum simple interest rate is [tex]\( \boxed{5} \)[/tex] years. Therefore, the correct answer is:
D. 5 years
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.