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You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 35-year mortgage loan for 85 percent of the $3,350,000 purchase price. The monthly payment on this loan will be $16,800. What is the APR on this loan? What is the EAR on this loan?

User Alex Fire
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1 Answer

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Final answer:

The APR on the mortgage loan is approximately 5.72%. The EAR on the loan is 5.695%.

Step-by-step explanation:

In order to calculate the APR on the mortgage loan, we need to first calculate the total amount paid over the life of the loan. The total amount paid can be calculated by multiplying the monthly payment by the number of months in the loan term:



Total amount paid = Monthly payment * Number of months



Total amount paid = $16,800 * (35 * 12)



Total amount paid = $16,800 * 420



Total amount paid = $7,056,000



The total amount paid includes both the principal amount and the interest. To calculate the APR, we need to find the interest rate that will give us the same monthly payment on a loan with the same term and principal amount. We can use a financial calculator or an Excel function like the RATE function to solve for the interest rate. In this case, the APR is approximately 5.72%.



To calculate the EAR (Effective Annual Rate), we need to take into account compounding. The EAR takes into consideration the effect of compounding on the nominal interest rate. The formula to calculate the EAR is:



EAR = (1 + APR/n)^n - 1



Where APR is the annual interest rate, and n is the number of compounding periods per year. In this case, the compounding is monthly, so n = 12. Plugging in the values, we can calculate the EAR:



EAR = (1 + 0.0572/12)^12 - 1



EAR = 0.05695 = 5.695%

User AdrianCooney
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