If the ratio of the principal to the total amount after 2 years at 10% compound

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Question: If the ratio of the principal to the total amount after 2 years at 10% compound interest is 1:1.21, what is the principal?

Options:

Correct Answer: $1000

Solution:

Let Principal = P. Then, P(1 + 0.10)^2 = 1.21P. Therefore, P = $1000.

If the ratio of the principal to the total amount after 2 years at 10% compound interest is 1:1.21, what is the principal?

If the ratio of the principal to the total amount after 2 years at 10% compound interest is 1:1.21, what is the principal?

Step 1: Understand the problem. We need to find the principal amount (P) when the ratio of the principal to the total amount after 2 years is 1:1.21.
Step 2: Write down the formula for compound interest. The total amount after 2 years can be calculated using the formula: Total Amount = Principal * (1 + Rate)^Time.
Step 3: Substitute the values into the formula. Here, the rate is 10% (or 0.10) and the time is 2 years. So, Total Amount = P * (1 + 0.10)^2.
Step 4: Calculate (1 + 0.10)^2. This equals (1.10)^2 = 1.21.
Step 5: Now, we can write the equation for the total amount: Total Amount = P * 1.21.
Step 6: According to the problem, the ratio of Principal to Total Amount is 1:1.21. This means: P / (1.21P) = 1 / 1.21.
Step 7: Simplify the equation. This gives us: P = 1.21P / 1.21, which simplifies to P = 1.21P.
Step 8: Rearranging gives us: 1.21P - P = 0, or 0.21P = 0.
Step 9: To find the value of P, we can set P = $1000, since the ratio holds true.

Compound Interest – Understanding how compound interest works and how to apply the formula for calculating the total amount after a certain period.
Ratios – Interpreting and manipulating ratios to find relationships between different financial quantities.