133k views
2 votes
Suppose you want to borrow $350000 to purchase a house. The loan has a term of 30 years and a nominal rate of 6% with monthly payments. The first payment is due one month from today. Suppose you pay 4% in origination fees at closing. What is the effective APR?

User OBlank
by
7.9k points

1 Answer

3 votes

The effective APR for the loan is 84.69%.

How to solve

To calculate the effective APR, we need to consider the origination fees and the monthly compounding of interest.

Step 1: Calculate the origination fees

Origination fees = 4% x $350,000 = $14,000

Step 2: Calculate the loan amount after origination fees

Loan amount = $350,000 - $14,000 = $336,000

Step 3: Calculate the monthly interest rate

Nominal rate = 6% per year = 0.5% per month

Step 4: Calculate the total number of payments

Number of payments = 30 years x 12 months/year = 360 months

Step 5: Calculate the monthly payment using the loan amount, interest rate, and number of payments

Monthly payment = $336,000 x (0.005 / (1 - (1 + 0.005)^-360)) = $1,726.64

Step 6: Calculate the total amount paid over the life of the loan

Total amount paid = Monthly payment x Number of payments = $1,726.64 x 360 months = $621,590.40

Step 7: Calculate the effective APR

Effective APR = (Total amount paid - Loan amount) / Loan amount * 100%

Effective APR = ($621,590.40 - $336,000) / $336,000 x 100% = 84.69%

Therefore, the effective APR for the loan is 84.69%.

User KAnNaN
by
7.8k points