A borrower takes out a 30-year mortgage loan for $100,000 with an interest rate of 6% plus 2 points. What is the effective annual interest rate on the loan if the loan is carried for all 30 years

EAR = 6.4%

Explanation:

Loan amount = 100000

Mortgage rate = 6%

2 Points = 2% * 100000 = 2000

Years = 30

Monthly rate = 0.50%

No of period = 360

PMT = PMT[Rate, N, -Loan)

PMT = PMT(0.50%, 360, -100000)

PMT = 599.55

Net loan amount = 100,000 - 2,000 = $98,000

Monthly cost = Rate [N, PMT, Net loan]

Monthly cost = Rate[360, 599.55, -98000)

Monthly cost = 0.515790%

Effective annual rate = (1 + 0.515790%)^12 - 1

Effective annual rate = 1.00515790^12 - 1

Effective annual rate = 1.06368120129 - 1

Effective annual rate = 0.06368120129

Effective annual rate = 6.4%

20,000 records should be looked

Solution:

Solve for s :  50 = [1.96*s/0.5]

25 = 1.96s

s = 12.75

Solve for "n":  n = [1.96*12.75/0.25]^2

n = [100]^2

n = 20,000