Question

When you purchased your house 4 years ago, you took out a $300,000, 30 year FRM loan at 7.5%. You also paid 2 points to get this loan. Now you want to sell your house and buy another one. In order to do so, you must pay off the existing one. The loan came with 1% prepayment penalty. What has been your effective interest rate on this loan? (show work)

Answer 1

When the loan was taken 4 years ago, we received a cash flow of $300,000
We also paid a 2% fee to get this loan, which means we paid 2% of $300,000 = $6,000

We build a loan amortizing schedule
We use the PMT function of Excel to compute annual payments. We calculate interest. Payments - Interest is the principal repaid in each period. In the next period, interest is charged on the outstanding balance in the previous period.
Hence we see that the interest goes on decreasing while principal repayment goes on increasing.

In year 0, that is today, to repay the loan, we have to pay the entire outstanding amount. We also have to pay a 1% prepayment penalty on the outstanding amount.

We calculate each year's cash flows. Essentially, the IRR of these cash flows is our effective rate of interest. Calculations are shown in the below table.

Loan amount	$        300,000
Tenure	30
Rate of interest	7.50%
Processing fee	2%
Prepayment penalty	1%
Year	-4	-3	-2	-1	0
Loan	$        300,000
Processing fee	$          (6,000)
Mortgage payment		$        (25,401)	$    (25,401)	$    (25,401)	$    (25,401)
Interest		$           (22,500)	$       (22,282)	$       (22,048)	$       (21,797)
Principal repayment		$             (2,901)	$         (3,119)	$         (3,353)	$         (3,604)
Outstanding principal		$          297,099	$      293,980	$      290,627	$      287,022
Prepayment penalty					$      (2,870)
Prepay principal					$ (287,022)
Net cash flows	$        294,000	$        (25,401)	$    (25,401)	$    (25,401)	$ (315,294)
Effective interest rate	8.33%

Hence effective interest rate on this loan is 8.33%