Question

Property worth ​$249 comma 000.00 can be purchased for 8​% down and monthly mortgage payments of $ 1500.00 for 25 years. What effective annual rate of interest is​ charged?

The effective annual rate of interest is ______%.

Answer 1

Value of property = $249,000

Down payment = 8% * $249,000
Down payment = $19,920

Amount borrowed = $249,000 - $19,920
Amount borrowed = $229,080

Monthly payment = $1,500
Time period = 25 years or 300 months

Let monthly interest rate be i%

$229,080 = $1,500 * PVIFA(i%, 300)

Using financial calculator:
N = 300
PV = -229080
PMT = 1500
FV = 0

I = 0.514%

Monthly interest rate = 0.514%

Effective annual rate = (1 + Monthly interest rate)^12 - 1
Effective annual rate = (1 + 0.00514)^12 - 1
Effective annual rate = 1.0635 - 1
Effective annual rate = 0.0635 or 6.35%