Home loans typically involve “points,” which are fees charged by the lender. Each point charged means that the borrower must pay 1% of the loan amount as a fee.

Home loans typically involve “points,” which are fees charged by the lender. Each point charged means that the borrower must pay 1% of the loan amount as a fee. For example, if the loan is for $140,000 and 3 points are charged, the loan repayment schedule is calculated on a $140,000 loan but the net amount the borrower receives is only $135,800. Assume the interest rate is 1.25% per month. What is the effective annual interest rate charged on such a loan, assuming loan repayment occurs over 312 months?




Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

First, compute the monthly payment on a $140,000 loan using the monthly interest rate provided:

PV	=	C((1 / r) – {1 / [r(1 + r)t]})
$100,000	=	C × ((1 / .0125) – {1 / [.0125(1.0125)312]})
	=	$1,787.06

Enter

312

1.25

–140,000

N

I/Y

PV

PMT

FV

Solve for

1,787.06

Second, compute the monthly interest rate based on the actual amount received and the loan payment calculated above.

PV	=	C((1 / r) – {1 / [r(1 + r)t]})
$135,800	=	$1,787.06 × ((1 / r) – {1 / [r(1 + r)312]}

To solve for r, it is easiest to use either a financial calculator or a computer. Here is the calculator solution based on a monthly period of time:

Enter

312

135,800

–1,787.06

N

I/Y

PV

PMT

FV

Solve for

1.292

Thus, the actual monthly interest rate is 1.292%.
Lastly, compute the effective annual rate as follows:

EAR	=	(1 + Monthly interest rate)12 – 1
	=	1.0129212 – 1
	=	0.1665, or 16.65%