Question 1171887: As debt payment, Php315,000 is due in 4 years and 7 months. If the debtor wishes to repay the debt now, and the lender applies 9% interest compounded semi annually when discounting debts, how much does he have to pay? *
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's how to solve this problem:
**Understanding the Problem**
We need to find the present value of a future debt payment. This involves discounting the future value back to the present using the given interest rate and compounding frequency.
**Steps**
1. **Convert Time to Years:**
* 4 years and 7 months is equal to 4 + (7/12) years = 4.5833 years.
2. **Calculate the Number of Compounding Periods:**
* Since the interest is compounded semi-annually (twice a year), the total number of periods is:
* 4.5833 years * 2 periods/year = 9.1666 periods.
* Since we are dealing with compounding, and payments, we must round the number of periods to the closest half period. Therefore, we should use 9.5 periods.
3. **Calculate the Periodic Interest Rate:**
* The annual interest rate is 9% (0.09), so the semi-annual interest rate is:
* 0.09 / 2 = 0.045
4. **Calculate the Present Value:**
* Use the present value formula:
* PV = FV / (1 + r)^n
* Where:
* PV = Present Value
* FV = Future Value (Php 315,000)
* r = Periodic Interest Rate (0.045)
* n = Number of Periods (9.5)
* PV = 315000 / (1 + 0.045)^9.5
* PV = 315000 / (1.045)^9.5
* PV = 315000 / 1.5034604
* PV ≈ 209516.63
**Answer**
The debtor has to pay approximately Php 209,516.63 now.
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