A person deposited Rs. 4000 in a bank at 6% compounded continuously. After 3 years, the rate of interest was increased to 7% and after 5 more years, the rate was further increased... A person deposited Rs. 4000 in a bank at 6% compounded continuously. After 3 years, the rate of interest was increased to 7% and after 5 more years, the rate was further increased to 8%. The money was withdrawn at the end of 10 years. Find the amount. Read more

Steps to Solve

1. Calculate the amount after the first 3 years at 6% interest To find the amount after 3 years with continuous compounding at a rate of 6%, use the formula:

$$ A = Pe^{rt} $$

Where:

• ( P = 4000 ) (initial deposit)
• ( r = 0.06 ) (annual interest rate)
• ( t = 3 ) (time in years)

Substituting these values in:

$$ A = 4000 e^{0.06 \times 3} $$

2. Calculate the amount after the next 5 years at 7% interest Now, we need to use the amount obtained from the first step as the principal for the next 5 years at an interest rate of 7%.

Let the amount at the end of 3 years be ( A_3 ):

$$ A_3 = 4000 e^{0.18} $$

Now, applying the formula for 5 years at 7%:

$$ A = A_3 e^{rt} = A_3 e^{0.07 \times 5} $$

Substituting:

$$ A = (4000 e^{0.18}) e^{0.35} = 4000 e^{0.53} $$

3. Calculate the amount after the last 2 years at 8% interest Now, we will apply the last interest rate of 8% for 2 more years. The amount at the end of 8 years will be:

$$ A_8 = 4000 e^{0.53} $$

Then, we find the total amount after 2 more years at 8%:

$$ A = A_8 e^{0.08 \times 2} = (4000 e^{0.53}) e^{0.16} = 4000 e^{0.69} $$

4. Calculate the final amount Now, compute the final amount:

$$ A = 4000 e^{0.69} $$

Use a calculator to find ( e^{0.69} \approx 1.993 ):

$$ A \approx 4000 \times 1.993 \approx 7972 $$