If compound interest received on a certain amount in the 3rd year is Rs. 12,100, what will be the compound interest for the 4th year if the rate of interest is 9%? The amount recei... If compound interest received on a certain amount in the 3rd year is Rs. 12,100, what will be the compound interest for the 4th year if the rate of interest is 9%? The amount received at 10% per annum compound interest after 3 years is Rs 10,648. What was the principal? In how many years will Rs 25,000 yield Rs 8,275 as compound interest at 10% per annum compounded annually? Read more

Steps to Solve

1. Determine Compound Interest for the 4th Year

The compound interest for each year is calculated as the interest on the principal at the given rate. The interest for the 4th year can be found using the formula:

$$ CI_{n} = P \times (1 + r)^n - P \times (1 + r)^{n-1} $$

Here, ( CI_{3} = 12,100 ) (given), and ( r = 9% = 0.09 ).

To find ( P ), we first need the total amount after 3 years, which is:

$$ A_{3} = P \times (1 + r)^3 $$

We can rearrange to find ( A_{4} ):

$$ A_{4} = A_{3} \times (1 + r) $$

Thus,

$$ CI_{4} = A_{4} - A_{3} $$

2. Calculate Total Amount After 3 Years

To calculate ( P ) based on the previous interest:

$$ A_{3} = P \times (1 + 0.1)^3 $$

Given ( A_{3} = 10,648 ):

$$ 10,648 = P \times (1.1)^3 $$

Calculating ( (1.1)^3 ):

$$ (1.1)^3 = 1.331 $$

Thus,

$$ P = \frac{10,648}{1.331} \approx 8000 $$

3. Determine the Time to Yield Rs 8,275 Interest

According to the compound interest formula, total amount ( A ) is given by:

$$ A = P \times (1 + r)^n $$

Where ( CI = A - P = 8,275 ).

So:

$$ A = 25,000 + 8,275 = 33,275 $$

Now, substituting this into the equation:

$$ 33,275 = 25,000 \times (1 + 0.1)^n $$

To solve for ( n ), divide both sides by 25,000:

$$ \frac{33,275}{25,000} = (1.1)^n $$

Calculating the left-hand side:

$$ 1.331 = (1.1)^n $$

Taking logarithm on both sides to solve for ( n ):

$$ n = \frac{\log{1.331}}{\log{1.1}} $$

4. Final Calculation

Compute the value of ( n ).