45. Mr. Ali invests Rs. 400,000 at the start of each quarter @ $$ 12 \% $$ for 8 years. What will be the total amount after 8 years? A) Rs. $$ 4,919,877 $$ B) Rs.5,510,263 C) Rs. $$ 211,001,103 $$ D) Rs. 21631137

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UpStudy AI · Accepted Answer

To determine the total amount Mr. Ali will have after 8 years, we'll use the **Future Value of an Annuity Due** formula. Since Mr. Ali invests at the **start** of each quarter, it's an annuity due scenario.

### Given:
- **Investment per quarter (P):** ₹400,000
- **Annual interest rate:** 12%
- **Quarterly interest rate (r):** 12% / 4 = 3% = 0.03
- **Number of years:** 8
- **Total number of quarters (n):** 8 * 4 = 32

### Formula:
$$ 
\text{Future Value (FV)} = P \times \left(\frac{(1 + r)^n - 1}{r}\right) \times (1 + r) 
$$

### Plugging in the values:
$$
\begin{align*}
\text{FV} &= 400,000 \times \left(\frac{(1 + 0.03)^{32} - 1}{0.03}\right) \times 1.03 \
&= 400,000 \times \left(\frac{2.591625 - 1}{0.03}\right) \times 1.03 \
&= 400,000 \times \left(\frac{1.591625}{0.03}\right) \times 1.03 \
&= 400,000 \times 53.054167 \times 1.03 \
&≈ 400,000 \times 54.645792 \
&≈ ₹21,858,317
\end{align*}
$$

### Closest Option:
The closest provided option to ₹21,858,317 is:

**D) ₹21,631,137**

**Answer:**  
**D) Rs. 21,631,137**
The total amount after 8 years is approximately Rs. 21,631,137.

Mr. Ali invests Rs. 400,000 at the start of each quarter @ for 8 years. What will be the total amount after 8 years?
A) Rs.
B) Rs.5,510,263
C) Rs.
D) Rs. 21631137

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Mr. Ali invests Rs. 400,000 at the start of each quarter @ for 8 years. What will be the total amount after 8 years? A) Rs. B) Rs.5,510,263 C) Rs. D) Rs. 21631137