Question

Suppose that you are purchasing a house (loan amount = $200,000) and inquire about the terms for a 30-year fixed-rate mortgage.

LOAN A:

• annual interest rate of 3.75% with monthly payments and compounding
• no discount points
• origination fee of 0.75%
• $928 in third-party closing costs

What is the Effective Borrowing Cost for loan A assuming no prepayment? What is the EBC for the loan if we prepay at the end of the third year?

Answer 1

Origination fee= 0.75% of $200,000 = $1,500

Also, the third -part closing = $928

Therefore, total up-front cost = 1,500+928 = $2,428

So, the net loan amount given = $200,000+$2,428 = $ 202,428

The emi for the loan amount $202,428 will be = $937.48 {done on excel sheet by using formula "=PMT(rate, nper, pv)", where rate is "3.75%/12, nper is "30*12" and PV is "$202,428"}

Now the effective interest rate will be = 3.85% , assuming emi to be $937.48, loan amount of $200,000 and payment period 30 years. {it is done on excel by using formula "=rate(nper, pmt, pv)", where nper is "30*12", pmt is "-937.48" and pv is "$200,000"

Therefore, Effective Borrowing Cost (EBC) for loan A assuming no prepayment is 3.85%.

Calculation of EBC in case the loan is pre-paid at the end of 3rd year

The total amount paid by the borrower = ($937.48*18) + $202,428 = $219,302.64

Therefore EBC = Interest paid/ (Principal*Time) = 19,302.64/ (200,000*3) = 3.22%

Therefore, Effective Borrowing Cost (EBC) for loan A assuming prepayment at the end of third year is 3.22%.