FINANCE

You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 35-year mortgage loan for 75 percent of the $3,250,000 purchase price. The monthly payment on this loan will be $15,800.

Requirement 1:
What is the APR on this loan? (Round your answer as directed, but do not use rounded numbers in intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

Requirement 2:
What is the EAR on this loan? (Round your answer as directed, but do not use rounded numbers in intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

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  1. PV of loan = .75(3250000) = $2,437,500
    paym = 15800
    n = 12(35) =420
    let the monthly rate be i
    2437500 = 15800( 1 - (1+i)^-420)/i
    154.2721519 i = 1 - (1+i)^-420

    This is a very nasty equation to solve.
    Back in the "good ol' days", we used a method called interpolation, and it took forever to do something like this.
    Often there there tables and charts, but that n = 420 would have been beyond most of the n values in the chart, so that caused further problems.

    I assume you have access to some software or calculator technology that will solve this for you.
    Using Wolfram, I got i = .00594417
    http://www.wolframalpha.com/input/?i=154.2721519+x+%3D+1+-+(1%2Bx)%5E-420
    - notice I changed the i to x, it assumed i was a complex number.

    check:
    15800( 1-1.00594417)^-420)/.00594417
    = 2,437,501.39
    not bad, off by about $1 in 2 1/2 million!!

    so if i = .00594417, then 12i = .07133
    or 7.13% per annum compounded monthly

    for b) I would simply find the annual rate j, so that

    1+j = 1.00594417^12
    j = .0737088...
    So the effective annual rate is 7.37%

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