Please help! Just need the answer...

A lender gives you a choice between the following two 30-year mortgages of $200,000:
Mortgage A: 6.65% interest compounded monthly, one point, monthly payment of $1283.93
Mortgage B: 6.8% interest compounded monthly, no points, monthly payment of $1303.85
Assuming that you can invest money at 5.6% compounded monthly, determine the length of time you must retain the mortgage in order for mortgage A to be the better choice. (Round your answer to two decimal places.)

PLEASE

To determine the length of time you must retain the mortgage in order for Mortgage A to be the better choice, you need to compare the net present values (NPVs) of both mortgages.

The NPV is calculated using the formula:

NPV = PV - FV,

where PV is the present value (the sum of all discounted cash flows) and FV is the future value.

We'll calculate the NPV for both Mortgage A and Mortgage B and find the period at which Mortgage A has a higher NPV.

1. Calculate NPV for Mortgage A:
Since Mortgage A has a one-point cost, the present value (PV) of Mortgage A is $200,000 - 1% of $200,000, which is $198,000.
The monthly payment for Mortgage A is $1283.93 for 30 years, which gives us a total of 30 * 12 = 360 payments.
The interest rate is 6.65% per year, compounded monthly, which gives us a monthly interest rate of 6.65% / 12 = 0.00554.
The future value (FV) of Mortgage A can be calculated using the formula: FV = PV * (1 + r)^n, where r is the monthly interest rate and n is the number of periods.
Hence, FV = $198,000 * (1 + 0.00554)^360 = $605,373.03.
Now, we can calculate the NPV for Mortgage A: NPV = PV - FV = $198,000 - $605,373.03 = -$407,373.03.

2. Calculate NPV for Mortgage B:
The present value (PV) for Mortgage B is the same as the loan amount, which is $200,000.
The monthly payment for Mortgage B is $1303.85 for 30 years, which gives us a total of 30 * 12 = 360 payments.
The interest rate is 6.8% per year, compounded monthly, which gives us a monthly interest rate of 6.8% / 12 = 0.00567.
The future value (FV) can be calculated using the formula: FV = PV * (1 + r)^n, where r is the monthly interest rate and n is the number of periods.
Hence, FV = $200,000 * (1 + 0.00567)^360 = $623,234.29.
Now, we can calculate the NPV for Mortgage B: NPV = PV - FV = $200,000 - $623,234.29 = -$423,234.29.

3. Compare the NPVs:
To determine when Mortgage A becomes the better choice, we need to find the period at which its NPV becomes positive, while Mortgage B's NPV is still negative.
Since the monthly interest rate on investments is 5.6% / 12 = 0.00467, we can calculate the NPV for Mortgage A after t periods using the formula: NPV = PV - FV / (1 + r^t), where r is the monthly interest rate.
Hence, NPV for Mortgage A = -$407,373.03 / (1 + 0.00467)^t.
We need to find the value of t when NPV for Mortgage A is zero, assuming t is in months: -$407,373.03 / (1 + 0.00467)^t = 0.
Solving this equation will give us the time period required.

To solve this equation, you can use a numerical method like trial and error, or you can use a solver function in tools like Excel or Google Sheets. Using trial and error, you can try different values for t until you find the one that makes the equation approximately zero. Keep narrowing the range until you find the answer.

Once you determine the value of t, remember to round it to two decimal places, as mentioned in the question.