Question
Asked Mar 2, 2019
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I need a detailed explanation of solving this problem:

You have purchased a new warehouse. To finance the purchase, you obtained a 25-year mortgage for 75% of $3,000,000 purchase price. The monthly payment will be $17,100.

a) What is the APR?

b) What is the EAR

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Expert Answer

Step 1

APR: It is abbreviated as Annual Percentage Rate, is a method for estimating the total cost a loan providers charges every year for the funds.

EAR: It is abbreviated as Effective Annual Rate is the interest cost that is balanced for compounding in a given period of time.

Step 2

a) Calculation of APR:

The APR can be calculated using a excel function =RATE, which denotes the interest rate of any investment. The need of using a excel function here is to get accurate final answers without any rounding error. In other words, for approximation the excel function is used here. The final answers are rounded to 2 decimal points. For example 11.5697% is rounded as 11.57%.

The amount of financing is $2,250,000 which is nothing but 75% of $3,000,000. Because 75% from the purchase price of $3,000,000 is financed under the mortgage. Hence, the periodic monthly payments are $17,100, and the number of years is 25 years. Since the mortgage is compounded monthly, the total number of periods of the mortgage is 300 months (which is nothing but 30 years * 12 months). The monthly payments of $17,100 are applied as “PMT”, the number of months of 300 is applied as “NPER” and the financing amount of $2,250,000 is applied as “PV”. There is no future value hence it is mentioned as 0. By using the excel function =RATE, the result obtained is 7.82% (0.65% per month). The excel spreadsheet is shown below:

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Step 3

The excel workings for calculating APR is shown below...

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