Question 1173770
Here's how to calculate the required monthly deposit and the total interest earned:

**a) Monthly Deposit**

* **Future Value (FV):** PKR 800,000,000
* **Annual Interest Rate (r):** 8% or 0.08
* **Number of Years (t):** 10
* **Compounding Periods per Year (n):** 12 (monthly)

1.  **Calculate the Monthly Interest Rate (i):**
    * i = r / n = 0.08 / 12 ≈ 0.006667

2.  **Calculate the Total Number of Periods (nt):**
    * nt = n * t = 12 * 10 = 120

3.  **Use the Sinking Fund Formula:**
    * PMT = FV * [i / ((1 + i)^nt - 1)]
    * PMT = 800,000,000 * [0.006667 / ((1 + 0.006667)^120 - 1)]
    * PMT ≈ 800,000,000 * [0.006667 / (2.219416 - 1)]
    * PMT ≈ 800,000,000 * [0.006667 / 1.219416]
    * PMT ≈ 800,000,000 * 0.005467
    * PMT ≈ 4,373,600 PKR

Therefore, the city needs to deposit approximately **PKR 4,373,600** each month.

**b) Total Interest Earned**

1.  **Calculate the Total Amount Deposited:**
    * Total Deposited = Monthly Deposit * Number of Payments
    * Total Deposited = 4,373,600 * 120 = 524,832,000 PKR

2.  **Calculate the Total Interest Earned:**
    * Total Interest = Future Value - Total Deposited
    * Total Interest = 800,000,000 - 524,832,000 = 275,168,000 PKR

Therefore, the total interest earned will be approximately **PKR 275,168,000**.

**Using the provided code result to verify**

The code provided the results.
Monthly deposit required: PKR 4372874.22
Total interest earned: PKR 275255094.19

The answers are very close to the manually calculated answers. The small difference is due to rounding during the manual calculation.