If the simple interset for 6 years be equal to 30 % of the princpal, it will be equal to the principal after

Options

A. 2 years
B. 30 years
C. 10years
D. 22 years

Answer

To solve the problem step by step, we need to find out how many years it will take for the simple interest to equal the principal amount, given that the simple interest for 6 years is equal to 30% of the principal.

### Step 1: Understand the given information
We know that the simple interest (SI) for 6 years is equal to 30% of the principal (P).

### Step 2: Calculate the annual simple interest
Since the simple interest is the same every year, we can find the annual interest rate.

Given:
- SI for 6 years = 30% of P
- SI for 1 year = (30% of P) / 6 = 5% of P

### Step 3: Determine how much interest is needed to equal the principal
To find out when the total interest will equal the principal, we need to know how much interest we need.

If the principal is 100% (let's assume P = 100), then we need an interest of 100% to equal the principal.

### Step 4: Calculate the total interest required
To equal the principal, we need:
- Total interest required = Principal = 100% of P

### Step 5: Find out how many years it will take to accumulate that interest
Since we earn 5% interest per year, we can set up the equation:
- Total interest = Annual interest × Number of years
- 100% = 5% × Number of years

### Step 6: Solve for the number of years
Now, we can solve for the number of years (let's call it T):
- 100% = 5% × T
- T = 100% / 5%
- T = 20 years

### Conclusion
It will take 20 years for the simple interest to equal the principal.

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