Question

Jim wants to buy a property and needs to borrow 195,000. He can get a loan at 7% for 25 years. Loan origination fees will be $4,700. Assume the lender also imposes a prepayment penalty of 3 percent of the outstanding loan balance if the loan is repaid within 8 years of closing. If Jim repays the loan after 6 years with the penalty, what is the effective interest rate?

8.1%

7.0%

7.9%

7.5%

Answer 1

The values given in the question are as follows:

• Loan amount = $195000
• Tenor of loan = 25 years
• Interest rate = 7% per annum
• Loan origination fees = $4700
• Prepayment penalty if loan repaid within 8 years = 3% of outstanding
• Loan prepayment period = 6 years

Effective interest rate (EIR) refers to the actual interest rate that a borrower effectively pays after including all forms of fees and costs such as origination fees, prepayment penalty etc.

The process of calculating EIR is as follows:

1. Calculate EMI for full term loan without any deductions
2. Calculate the outstanding loan amount at the end of the prepayment period
3. Deduct any origination fees from loan amount for net loan amount as well as include any penalty in outstanding loan payment
4. Calculate the effective interest rate using the new values using Excel or a financial calculator

The table below shows the calculation using excel:

Initiation of Loan
Loan	195000	$	PV
Interest rate	7%	per annum
	0.58%	per month	Rate
Years of Loan	25	years
	300	months	N
EMI	-1,378.22	$	Using Excel PMT function
Thus, Jim would be required to make a payment of $1,378.22 every month to service the loan
After 6 years
Remaining loan term	19	years
	228	months
Value of loan	173,537	$	Using Excel PMT function
Thus, Jim would have an outstanding loan of $173,537 at the end of 6 years
To calculate Effective Interest Rate
Loan Amount	195000
Loan origination fees	4700
Net proceeds from loan	190300		Effective PV
Loan outstanding after 6 years	173,537
Prepayment penalty	3%	of outstanding
Prepayment penalty	5,206	$
Total payment after 6 years	178,743		Effective FV
Prepayment period	6	years
	72	months	Effective N
EMI	1,378.22	$	PMT constant
Effective interest rate	0.66%	per month
Effective interest rate	7.90%	per annum

Thus, the effective interest rate is 7.9%