Please help me with the areas in bold below but if you can assist on the entire problem and explain it in detail that would be great :)

On January 2013, Professor Xin buys a house. Here is the information

Price = 250,000

LTV (loan to value) = 80%

Interest Rate = 8%

Other cost = 4%

1. What is the effective interest rate?

The monthly payment is : 1,467.53

If PV = 192000, PMT = -1467.53, n = 360

Solve for i = 8.44

2. If from January 2013, Professor Xin plans to sell his house after 15 years. What is the effective interest rate for Professor Xin in Jan2013?

PV = 192,000

FV = -153,563.12

PMT = -1,467.53

N = 180

Solve for i = 8.509

3. From January 2013, after 8 years, the market interest rate is 7.5%, do you suggest Professor Xin to refinance his house (if the bank agrees to refinance for 22 years, and charge 4% of cost for refinance)?

Here is the calculation:

After 8 years (Dec 2020), the balance is 182,035.40 <= (how do you calculate this number?)

I = 7.5, n = 22*12 = 264.   We get monthly payment

1,409.88   (How does 182,035.40 affect this calculation? Is it FV or PV?)

The real money Professor Xin gets from the bank:

182,035.40 * 96% = 174,754

We can get the effective interest rate

PV = 174,754

PMT = -1,409.88

N = 22 * 12 = 264

Solve for i = 8.004     which is greater than 8 %