# Math Help - solve for interest rate

1. ## solve for interest rate

Trying to figure out, without the use of an excel function how to solve for an interest rate of a mortgage knowing the following paramaters.

initial principal balance - 200,000
total interest paid - 279,017.80
years amortized - 30
payments/yr - 12

If it helps any the answer is 7%.

I use the RATE function in excel and it works fine, but again trying to solve without that function.. Thank you!

John

2. initial principal balance - 200,000
total interest paid - 279,017.80
years amortized - 30
payments/yr - 12
The formula for a standard mortgage is Payment * (1-vⁿ)/i = L

Where Payment is the monthly payment, v = 1/1+i, i is your effective interest rate, and L is the Loan Amount.

Total Interest paid is the Number of Payments you will make minus the loan amount. Let our Monthly Payment be P, so we have 360P - 200,000 = 279,017.8. Solving for P, we get 1330.61 for our monthly payment on the Loan.

Taking our original loan equation, we have $1330.61 * \frac{1-v^{360}}{i} = 200000$

$\frac{1-v^{360}}{i} = 150.31$

$1 - (1 + i)^{-360} = 150.31i$

From here, you'd need logs/natural logs. Can you take it from here?

Also, to see more detail on a home loan payment proving 7% is your answer another way, use my mortgage calculator here:

http://www.mathcelebrity.com/mortgage.php

3. i was with you til the logs/natural logs part.. haha
I have someone putting this calculation into a program to calculate, so maybe she knows what to do w/ that formula... Unfortunately I don't even know what a log is (logarith?) if that was right, i must have just seen it on smarter than a 5th grader, and still am not sure how to do the calc, but let me check w/ our programmer and see if she does... thanks for the assistance so far. Thanks!

4. Originally Posted by slym34
i was with you til the logs/natural logs part.. haha
I have someone putting this calculation into a program to calculate, so maybe she knows what to do w/ that formula... Unfortunately I don't even know what a log is (logarith?) if that was right, i must have just seen it on smarter than a 5th grader, and still am not sure how to do the calc, but let me check w/ our programmer and see if she does... thanks for the assistance so far. Thanks!

Thinking about this and looking at Kellison's book, ignore what I said about logs. Your programmer needs to write an iteration program to solve for interest rate. That is the only way to solve for interest rate for annuities from what I read.

I'd show her the math for a Loan, and have her start at 0.0001 and add that until the Loan Amount equals what you want.

Also, plug in your information on my mortgage program and show her how 7% gives you the answer you want. Sometimes as programmers, she may want to back into the answer that way if she is writing code.

5. thanks I think that will work out.. I appreciate the assistance!

John