Question 1173770: A major city wants to establish a sinking fund to pay off debts of PKR 800 million which come due in 10 years. The city can earn interest at the rate of 8 percent per year compounded monthly. If first deposit is made 1 month from now;
a)What monthly deposit will be required to accumulate the PKR 800 million?
b)How much interest will be earned on these deposits
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! 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.
|
|
|
