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According to annual compound interest, where [tex]\( P \)[/tex] is the principal, [tex]\( R \)[/tex] is the rate of interest, and [tex]\( T \)[/tex] is the time, what will be the compound interest?

वार्षिक मिश्रित व्याज अनुसार मूलधन [tex]\( P \)[/tex], व्याजदर [tex]\( R \)[/tex], र समय [tex]\( T \)[/tex] भए मिश्र व्याज कति होला?

A. [tex]\(\frac{P \times T \times R}{100}\)[/tex]
B. [tex]\(P\left(1+\frac{R}{100}\right)^T\)[/tex]
C. [tex]\(P\left[\left(1+\frac{R}{100}\right)^T-1\right]\)[/tex]
D. [tex]\(P\left(1-\frac{R}{100}\right)^T\)[/tex]

Sagot :

GinnyAnsweridn
To solve for compound interest, we use the formula:

[tex]\[CI = P \left[\left(1 + \frac{R}{100}\right)^T - 1\right]\][/tex]

Here, [tex]\(CI\)[/tex] represents the compound interest, [tex]\(P\)[/tex] is the principal amount, [tex]\(R\)[/tex] is the annual rate of interest, and [tex]\(T\)[/tex] is the time in years.

Let's break down the steps to understand how this formula works:

1. Identify the Principal Amount (P): This is the initial sum of money that you have invested or loaned. For example, let’s assume [tex]\(P = 1000\)[/tex].

2. Determine the Rate of Interest (R): This is the percentage of interest you earn on the principal annually. Let's assume [tex]\(R = 5\% \)[/tex].

3. Specify the Time Period (T): This is the number of years for which the money is invested or borrowed. Let's assume [tex]\(T = 2\)[/tex] years.

4. Calculate the Compound Factor:
- First, we convert the interest rate from percentage to a decimal by dividing by 100:
[tex]\(\frac{R}{100} = \frac{5}{100} = 0.05\)[/tex]
- Then, add 1 to this decimal:
[tex]\(1 + 0.05 = 1.05\)[/tex]

5. Raise this compound factor to the power of time (T):
[tex]\((1.05)^2\)[/tex]

6. Subtract 1 from the result of step 5:
[tex]\((1.05)^2 - 1 = 1.1025 - 1 = 0.1025\)[/tex]

7. Multiply this result by the Principal (P):
[tex]\(1000 \times 0.1025 = 102.5\)[/tex]

Hence, the compound interest is given by:
[tex]\[CI = 102.5\][/tex]

So, the correct choice that represents the formula for calculating compound interest is:
[tex]\[c. \ P\left[\left(1+\frac{R}{100}\right)^T-1\right]\][/tex]
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