SOLUTION: Paul owes Winston R1000.00 due in Three years and R8000 due in five years. Paul wishes to reschedule his debt so as to pay two sums on different dates, one say x in one year and th

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Question 1196245: Paul owes Winston R1000.00 due in Three years and R8000 due in five years. Paul wishes to reschedule his debt so as to pay two sums on different dates, one say x in one year and the other 2x five years later. Winston agrees provided that the interest rate is 18% per annum compounded quarterly. What are Paul's payment?
Answer by ElectricPavlov(122) About Me  (Show Source):
You can put this solution on YOUR website!
**1. Find the Present Value of Paul's Current Debt**
* **Calculate the Present Value of R1000 due in 3 years:**
* **Quarterly Interest Rate:** 18% per annum / 4 quarters = 4.5% per quarter
* **Number of Quarters:** 3 years * 4 quarters/year = 12 quarters
* **Present Value:** R1000 / (1 + 0.045)^12 = R1000 / 1.71 = R584.79
* **Calculate the Present Value of R8000 due in 5 years:**
* **Number of Quarters:** 5 years * 4 quarters/year = 20 quarters
* **Present Value:** R8000 / (1 + 0.045)^20 = R8000 / 2.4117 = R3317.79
* **Total Present Value of Debt:** R584.79 + R3317.79 = R3902.58
**2. Set Up the Equation for the Rescheduled Debt**
* **Present Value of x due in 1 year:** x / (1 + 0.045)^4
* **Present Value of 2x due in 5 years:** 2x / (1 + 0.045)^20
* **Equation:**
* x / (1 + 0.045)^4 + 2x / (1 + 0.045)^20 = R3902.58
**3. Solve for x**
* **Simplify the equation:**
* x / 1.1925 + 2x / 2.4117 = R3902.58
* 0.8386x + 0.8295x = R3902.58
* 1.6681x = R3902.58
* **Calculate x:**
* x = R3902.58 / 1.6681
* x ≈ R2338.69
**4. Calculate the Second Payment**
* 2x = 2 * R2338.69 = R4677.38
**Therefore, Paul's rescheduled payments will be:**
* **R2338.69 due in one year**
* **R4677.38 due in five years**
**Note:** These calculations assume that the interest rate remains constant at 18% per annum compounded quarterly throughout the entire period.