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Figuring Out the Rate
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THE SCENARIO
I was looking at a mortgage this morning, and I was curious as to the interest rate the borrower is paying.
The loan has had regular monthly payments paid over the last 5 years, and $198,984.80 is owed today. The monthly payment is $1,504.59, which includes $454.28 in Escrow impounds (for property taxes and insurance). The loan amortizes fully over 30 years.
The question: What's the interest rate on this mortgage?
THE SOLUTION
This one is pretty straightforward. The only things we don't know are the monthly Principal and Interest (P&I) payment and the amount of time left on the loan.
To find P&I, we subtract the impounded amount ($454.28) from the total payment ($1,504.59) to get $1,504.59 - $454.28 = $1050.31.
To find the time left, we subtract the elapsed time (5 years is 5 x 12 = 60 months) from the original 30 years = 30 x 12 = 360 months.
360 - 60 = 300 months.
First things first, make sure the calculator is using 12 Payments per Year.
N: 300 (The loan has 300 monthly payments still due)
I/YR: (This is what I'm trying to find)
PV: 198,984.80 ($198,984.80 is owed today)
PMT: -1,050.31 (The monthly payment is $1,050.31)
FV: 0 (The loan amortizes fully)
The loan has an interest rate of 4.00%.
What do you think? Does that seem like a low rate to you? Or high, given the time frame in which it was originated? Let us know in the comments!
