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If the principal and compound interest are equal, how many times the principal is the compound amount?

Sagot :

GinnyAnsweridn
Certainly! Let's consider the problem step-by-step:

1. Define the Principal (P):
Let's assume the principal amount (P) is 1 unit. This keeps the calculations simple and straightforward.

2. Condition of the Problem:
According to the problem, the principal and the compound interest (CI) are equal. Hence, if the principal is 1 unit, the compound interest must also be 1 unit.

3. Calculate the Total Compound Amount (A):
The compound amount (A) is the sum of the principal (P) and the compound interest (CI).
[tex]\[ A = P + CI \][/tex]
Since [tex]\( P = 1 \)[/tex] and [tex]\( CI = 1 \)[/tex]:
[tex]\[ A = 1 + 1 = 2 \][/tex]

4. Find the Ratio of the Compound Amount to the Principal:
To determine how many times the compound amount (A) is in terms of the principal (P), we calculate the ratio:
[tex]\[ \text{Ratio} = \frac{A}{P} \][/tex]
Substituting the values we found:
[tex]\[ \text{Ratio} = \frac{2}{1} = 2 \][/tex]

Therefore, the compound amount is 2 times the principal.
Minavaidn
If the principal (P) and compound interest (CI) are equal, then the compound amount (A), which is the sum of the principal and the compound interest, would be twice the principal.

This is because:

\[
\text{Compound Amount (A)} = \text{Principal (P)} + \text{Compound Interest (CI)}
\]

Given that \(\text{CI} = \text{P}\), we have:

\[
\text{A} = \text{P} + \text{P} = 2\text{P}
\]

So, the compound amount is **two times** the principal.
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