what a deal!
Oh - was there a question in there somewhere?
$400,000 for 30-years at a fixed APR of 3.87%. The loan payments are monthly and interest is compounded monthly.
3 answers
What is the effective annual rate on the loan? (I.e., what is the interest rate once we take into account compounding?)
We don't need the principal nor the time to find the effective annual rate
All we are looking for it the annual rate i, which is equivalent to a rate of .0387/12 per month
that is,
(1+i)^1 = (1+.0387/12)^12
1+i = 1.0393939
i = .03939 or appr 3.939% (note, the decimals only appear to repeat at the beginning, they do not)
check: take 100 for 5 years
at 3.939..%
amount = 100(1.03939...)^5 = 121.315
at 3.87% compouned monthly,
amount = 100(1 + .0387/12)^60 = 121.31
well, how about that?
All we are looking for it the annual rate i, which is equivalent to a rate of .0387/12 per month
that is,
(1+i)^1 = (1+.0387/12)^12
1+i = 1.0393939
i = .03939 or appr 3.939% (note, the decimals only appear to repeat at the beginning, they do not)
check: take 100 for 5 years
at 3.939..%
amount = 100(1.03939...)^5 = 121.315
at 3.87% compouned monthly,
amount = 100(1 + .0387/12)^60 = 121.31
well, how about that?
4 answers