Mr. Rich secured a mortgage loan for $2.5 million, or 65 percent of the home's purchase price. The mortgage period is 30 years, with a $10,400 monthly payment. This loan's Effective annual rate is 6.82%.
When the benefits of compounding over time are taken into account, the real return on a savings account or any other interest-paying investment is known as the effective annual interest rate. It also displays the actual percentage rate of interest owed on any outstanding debts, including credit card debt and loans.
given data
loan = 65 % of $2.5 million = $1625000
monthly payment pmt = $10,400
time = 30 year = 30 × 12 = 360
First, we rate this based on its current value.
present value = pmt X [tex]\frac{1 - (1 + r)^{-t} }{r}[/tex]
$1625000 = $10400 X [tex]\frac{1 - (1 + r)^{-360} }{r}[/tex]
r = 0.5517%
Effective annual rate = [tex](1+ r)^{12} - 1[/tex]
Effective annual rate= [tex](1+ 0.005517)^{12} - 1[/tex]
Effective annual rate = 0.068250
Effective annual rate = 6.82 %
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