Bill has a debt of $5000 which was due 30 days ago.He also has another debt of $6000 due 90 days from now.It has been decided that these 2 debts will be settled by a payment of $4000 today and a final payment of X made 70 days from now.If the simple interest rate is r = 9%,what is the value of X if you use a focal date of now?
A)$7025.94
B)$7024.80
C)$7000.00
D)$6906.73

Question

Quizplus · Accepted Answer

The value of X can be calculated by first finding the present value (PV) of each debt at the focal date (now), then determining the future value (FV) of the $4000 payment made today, and finally calculating the value of X needed to settle the remaining balance.1. Calculate the present value of the $5000 debt due 30 days ago (which is actually a future value from the perspective of 30 days ago):$$ PV = \frac{FV}{(1 + rt)} = \frac{5000}{(1 + 0.09 \times \frac{30}{365})} = 5000 \times (1 - 0.09 \times \frac{30}{365}) \approx 4987.67 $$2. Calculate the present value of the $6000 debt due 90 days from now:$$ PV = \frac{FV}{(1 + rt)} = \frac{6000}{(1 + 0.09 \times \frac{90}{365})} = 6000 \times (1 - 0.09 \times \frac{90}{365}) \approx 5854.25 $$3. The total present value of the debts is:$$ 4987.67 + 5854.25 = 10841.92 $$4. The future value of the $4000 payment made today, 70 days from now, is:$$ FV = PV \times (1 + rt) = 4000 \times (1 + 0.09 \times \frac{70}{365}) \approx 4076.16 $$5. The remaining balance to be settled by the payment X, 70 days from now, is:$$ 10841.92 - 4076.16 = 6765.76 $$6. Since the payment X is also made 70 days from now, its present value today is equal to its nominal value (X). Therefore, to find X, we need to adjust the remaining balance back to its value 70 days from now:$$ X = 6765.76 \times (1 + 0.09 \times \frac{70}{365}) \approx 7025.94 $$Therefore, the value of X is approximately $7025.94.

Bill Has a Debt of $5000 Which Was Due 30