Final answer:
To determine the timing of the third payment with an interest rate of 9% compounded monthly, the present value of Graham's payment plans must be equalized using the formula for the present value of annuities. The monthly interest rate is 0.75% and the formula Present Value (PV) = Payment / (1 + i)^n is used, where i is the monthly interest rate and n is the number of months. Solving this equation will give the time, n, for the third payment.
Step-by-step explanation:
To address the question of when Graham should make the third payment if the interest rate is 9% compounded monthly, we need to equalize the present values of the original payment plan and the new payment plan. Given that the original payments were $14,000.00 each at 2 months, 7 months, and 10 months, and the new payments are $22,400.00 at 5 months, $10,000.00 at 15 months, and the third unknown payment, we can use the formula for the present value of annuities, compounded monthly, to solve for the time when the third payment occurs.
Let's calculate the present value of the original and renegotiated payments. To do this, we will use the formula: Present Value (PV) = Payment / (1 + i)^n, where i is the monthly interest rate and n is the number of months. The monthly interest rate is 9% annually, or 0.75% per month (9% / 12).
We now need to solve for n when the present value of the new payment plan equals the present value of the original payments. This requires setting up an equation and solving for n using logarithms or a financial calculator.