Question 1173649: 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! Absolutely, let's break down this sinking fund problem step-by-step:
**Understanding the Problem**
* **Future Value (FV):** PKR 800,000,000 (the amount needed in 10 years)
* **Annual Interest Rate (r):** 8% or 0.08
* **Compounding Frequency (n):** Monthly (12 times per year)
* **Time Period (t):** 10 years
**Calculations**
**a) Monthly Deposit Calculation**
1. **Monthly Interest Rate (i):**
* i = r / n = 0.08 / 12 = 0.00666667 (approximately)
2. **Total Number of Periods (N):**
* N = n * t = 12 * 10 = 120 months
3. **Sinking Fund Formula:**
* The monthly deposit (PMT) can be calculated using the following formula:
* PMT = FV * (i / ((1 + i)^N - 1))
4. **Applying the Values:**
* PMT = 800,000,000 * (0.00666667 / ((1 + 0.00666667)^120 - 1))
* PMT = 4,372,874.22 PKR
Therefore, the city will need to deposit approximately PKR 4,372,874.22 each month.
**b) Total Interest Earned**
1. **Total Deposits:**
* Total Deposits = PMT * N = 4,372,874.22 * 120 = 524,744,905.81 PKR
2. **Total Interest:**
* Total Interest = FV - Total Deposits = 800,000,000 - 524,744,905.81 = 275,255,094.19 PKR
Therefore, the city will earn approximately PKR 275,255,094.19 in interest over the 10 years.
**Summary**
* **Monthly Deposit:** PKR 4,372,874.22
* **Total Interest Earned:** PKR 275,255,094.19
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