Answer:
Annual Interest Rate, r = 5.69%
Step-by-step explanation:
Amount of loan taken = 220,000
Closing fee is 5% of the loan value
Closing fee = 5% of 222,000 = 0.05 * 220000 = 11000
Therefore, Principal, P = Loan amount + closing fee
P = 220000 + 11000
P = 231, 000
Annual rate, r= 5.25% = 0.0525
Monthly rate, i = 0.0525/12 = 0.004375
Time, n = 30 years = 30*12 = 360 months
The monthly payment will be calculated by:
[tex]PMT = \frac{P*i}{1 - (1 + i)^{-n}} \\\\PMT = \frac{231000 * 0.004375}{1 - (1 + 0.004375)^{-360}} \\\\PMT = 1275.59[/tex]
Assuming payments are made based on 220,000, let us calculate the monthly interest rate.
[tex]PMT = \frac{P*i}{1 - (1 + i)^{-n}} \\\\1275.59 = \frac{220000 * i}{1 - (1 + i)^{-360}} \\\\i = 0.00474229[/tex]
Annual rate, r = 12 * 0.0047429
r = 0.0569 = 5.69%
