SOLUTION: Paul owes Winston R1000 due in three years and R8000 due in five years. He wishes to reschedule so as to pay two sums on different dates, one say x in one year, and the other 2x fi

Algebra ->  Finance -> SOLUTION: Paul owes Winston R1000 due in three years and R8000 due in five years. He wishes to reschedule so as to pay two sums on different dates, one say x in one year, and the other 2x fi      Log On


   

Question 1196116: Paul owes Winston R1000 due in three years and R8000 due in five years. He wishes to reschedule 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 compound quarterly. What are Paul's payments?
Answer by ElectricPavlov(122) About Me  (Show Source):
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**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.