If a bank pays 12% interest compounded monthly, what equal deposits have to be made at the end of each month for 4 years if you want to have  ₹ 2,00,000 at the end of 4 years?


Select one:
 ₹ 3,466.67
 ₹ 3,366.66
 ₹ 3,266.77
₹ 3,666.66

To find the equal monthly deposits needed to accumulate ₹ 2,00,000 at the end of 4 years with 12% interest compounded monthly, we can use the formula for the future value of an ordinary annuity:

\[
A = P \times \left( \frac{(1 + r)^n - 1}{r} \right)
\]

Where:
- \( A \) is the future value (₹ 2,00,000).
- \( P \) is the monthly deposit.
- \( r \) is the monthly interest rate.
- \( n \) is the total number of periods.

Given:
- Future value \( A = ₹ 2,00,000 \)
- Annual interest rate \( i = 12\% = 0.12 \)
- The interest is compounded monthly, so the monthly interest rate \( r = \frac{0.12}{12} = 0.01 \)
- Time \( t = 4 \) years
- Number of periods \( n = 12 \times 4 = 48 \)

We need to solve for \( P \) (the monthly deposit). Rearrange the formula to solve for \( P \):

\[
P = \frac{A \times r}{(1 + r)^n - 1}
\]

Now, plug in the values:

\[
P = \frac{2,00,000 \times 0.01}{(1 + 0.01)^{48} - 1}
\]

Let's calculate this step by step.

1. Calculate \( (1 + 0.01)^{48} \):
\[
(1.01)^{48} \approx 1.601032
\]

2. Subtract 1 from the result:
\[
1.601032 - 1 = 0.601032
\]

3. Multiply \( A \) by \( r \):
\[
2,00,000 \times 0.01 = 2,000
\]

4. Divide by \( 0.601032 \):
\[
P = \frac{2,000}{0.601032} \approx 3,327.64
\]

This value is slightly off from the provided options, so let's refine:

Refined calculation:

\[
P \approx \frac{2,000}{0.601032} \approx 3,327.67
\]

However, since none of the options is exactly ₹ 3,327.67, we must choose the closest value. The closest option is **₹ 3,366.66**.

Thus, the correct answer is:

**₹ 3,366.66**

Would you like further details on this? Here are some related questions:

1. How does increasing the interest rate affect the required monthly deposit?
2. What would be the required deposit if the interest were compounded quarterly instead of monthly?
3. How does extending the time period to 5 years affect the monthly deposit amount?
4. What is the difference between simple interest and compound interest in terms of future value?
5. How can the future value of an annuity be adjusted if deposits are made at the beginning of each month?

**Tip:** Always ensure the compounding frequency matches the payment frequency when using annuity formulas.

Learn how to calculate equal monthly deposits required to accumulate ₹ 2,00,000 at the end of 4 years with 12% interest compounded monthly. Detailed step-by-step solution using the Future Value of an Annuity formula.

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