5-10 Home loans typically involve “points,” which are fees charged by the lender

Question

5-10

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 $190,000 and 2 points are charged, the loan repayment schedule is calculated on a $190,000 loan but the net amount the borrower receives is only $186,200. Assume the interest rate is 1.00% per month. What is the effective annual interest rate charged on such a loan, assuming loan repayment occurs over 252 months? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.Use a financial calculator or Excel.)

  Effective annual interest rate

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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 $190,000 and 2 points are charged, the loan repayment schedule is calculated on a $190,000 loan but the net amount the borrower receives is only $186,200. Assume the interest rate is 1.00% per month. What is the effective annual interest rate charged on such a loan, assuming loan repayment occurs over 252 months? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.Use a financial calculator or Excel.)

Explanation / Answer

Step 1: Calculate the Amount of Monthly Payment

The amount of monthly payment can be calculated with the use of PMT function/formula of EXCEL/Financial Calculator. The function/formula for calculating PMT is PMT(Rate,Nper,-PV,FV) where Rate = Fees, Nper = Period, PV PV = Value of Loan and FV = Future Value (if any).

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Here, Rate = 1%, Nper = 252, PV = $190,000 and FV = 0

Using these values in the above function/formula for PMT, we get,

Monthly Payment = PMT(1%,252,-190000,0) = $2,068.53

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Step 2: Calculate Nominal Monthly Rate

The monthly rate can be calculated with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,-PV,FV) where Nper = Period, PMT = Monthly Payment, PV = Net Amount Received and FV = Future Value (if any)

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Here, Nper = 252, PMT = $2,068.53, PV = $186,200 and FV = 0

Using these values in the above function/formula for PMT, we get,

Nominal Monthly Rate = Rate(252,2068.53,-186200,0) = 1.026%

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Step 3: Calculate Effective Annual Interest Rate

The effective annual interest rate can be calculated as follows:

Effective Annual Interest Rate = (1+Nominal Monthly Interest Rate)^12 - 1 = (1+1.026%)^12 - 1 = 13.03%

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