We Need To Equalize Total Payments And Total Obligation

We Need To Equate The Total Payments To The Total Obligations Due At T

We are tasked with calculating the total payments and obligations at the end of year three, ensuring they are equal by appropriately projecting debts and payments. The debts involved include R780 and R7,000, which need to be moved to the end of year three. Additionally, there are payments of R1,300 at the end of year one and an unknown payment R x at the end of year three. The goal is to find the value of R x that equates total payments and total obligations at year three.

Paper For Above instruction

Financial management often requires projecting liabilities and payments into future periods to ensure accurate assessment of financial obligations. In this scenario, the primary objective is to synchronize the total payments with the total obligations due at the end of year three. This involves calculating the future values of debts and payments using compound interest principles, specifically focusing on an annual interest rate of 11%.

Initially, the debts consist of R780 and R7,000, which, for proper comparison, must be projected to the end of year three. The future value of each debt is calculated using the compound interest formula:

FV = P (1 + R)^T

Where P is the present value, R is the interest rate per period, and T is the number of periods (years).

For the R780 debt, the future value at year three is computed as:

FV = 780 × (1 + 0.11)^1 = 780 × 1.11 = R865.80

This calculation assumes the debt accrues interest for one year to be moved to year three; however, it appears from the context that the debt was initially due earlier and is now projected to the end. The calculation indicates a single year of accumulation, but the real intention is to project to three years. For the purpose of this problem, we'll consider the debt as being overdue for one year and now accumulated for three years, so the calculation is adjusted accordingly:

FV = 780 × (1 + 0.11)^3 = 780 × 1.11^3 = 780 × 1.36763 ≈ R1,066. minuti

Similarly, for the R7,000 debt, the future value at year three is:

FV = 7,000 × (1 + 0.11)^3 = 7,000 × 1.36763 ≈ R9,573.41

Once these debts are projected to year three, the total obligations sum to:

Total obligations = 1,066 + 9,573.41 = R10,639.41

Next, the payments are considered. There are two payments: R1,300 at the end of year one and an unknown amount R x at the end of year three. The future value of the R1,300 payment is calculated to determine its worth at year three:

FV = P × (1 + R)^2 = 1,300 × (1 + 0.11)^2 = 1,300 × 1.2321 ≈ R1,601.73

The total payments at year three, considering the payments made, must equal the obligations at that time. Hence, the total obligations are equated to the sum of future payments:

R1,601.73 + R x = R10,639.41

Solving for R x yields:

R x = R10,639.41 – R1,601.73 ≈ R9,037.68

Therefore, the payment R x at year three should be approximately R9,037.68 to balance the total obligations with total payments, ensuring the financial liabilities are fully settled at year three.

References

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