2. Home loans typically involve \"points,\" which are fees charged by the lender

Question

2. 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 fo $100,000 and 2 points are charged, the loan repayment schedule is calculated on a $100,000 loar but the net anount the borrower receives is only $98,000. Assume the interest rate is8% pe year. What is the effective annual interest rate charged on such a loan, assuming loan repaymen occurs over 360 months? A) 0.65% B) 0.68% C) 7.79% D) 8.21%

Explanation / Answer

The loan amount is $100,000 and time period for loan is 360 month

We can use following Present Value of an Annuity formula to calculate the monthly loan payment with 8% interest rate on the loan

PV of loan = PMT * [1-(1+i) ^-n)]/i

Where,

Present value of loan (PV) = $100,000

Monthly loan payment PMT =?

Number of payments n = 360 months

Annual interest rate I =8%, therefore monthly interest rate i=8%/12 = 0.67%

Therefore

$100,000 = PMT * [1- (1+0.67%) ^-360]/0.67

Or PMT = $733.76

But we know that actual amount received as a loan is $98,000 after 2% bank fees deduction, therefore to calculate effective annual rate charged on such loan, assume that PV of loan is $98,000 and PMT is $733.76 than calculate interest rate of loan in following manner

Present value of loan (PV) = $98,000

Monthly loan payment PMT =$733.76

Number of payments n = 360 months

Annual interest rate I =? Therefore monthly interest rate i = I/12 =?

Therefore

$98,000 = $733.76 * [1- (1+i %) ^-360]/i%

From trial and error method, we can calculate the value of i; which is 0.6845% per month

Or 0.6845% *12 = 8.21% per annum

Therefore correct answer is option D. 8.21%

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