Question

Mr. Rich arranged for a mortgage loan for 65 percent of the $2.5 million purchase price of a home. The monthly payment will be $10,400 and the mortgage term is 30 years. What is the EAR on this loan?

Answer 1

Answer:

Effective annual rate = 6.82 %

Explanation:

given data

loan = 65 % of  $2.5 million = $1625000

monthly payment pmt = $10,400

time = 30 year = 30 × 12 = 360

solution

we get here rate first by present value

present value = pmt × $\frac{1-(1+r)^{-t}}{r}$   ..........1

$1625000 = $10400  × $\frac{1-(1+r)^{-360}}{r}$

15.625 = $\frac{1-(1+r)^{-360}}{r}$

solve it we get

r = 0.5517%

and Effective annual rate  will be

Effective annual rate = $(1+r)^{12} -1$

Effective annual rate = $(1+0.005517)^{12} -1$

Effective annual rate = 0.068250

Effective annual rate = 6.82 %