How do I calculate interest rate?

[gmblng]

Howdy - new to forum.
Thanks in advance for the help.

Need to calculate the interest rate.

I know the loan amount, the term, the yearly payment (and can figure out the monthly by dividing yearly by 12.). Need to find the % rate.

Does someone have a formula I can use? I need to show work and I can't find anything in my book or anywhere else - everyone keeps referring me to online calculators.

if you need specific numbers, I can provide them but want to try to solve on my own.

Thanks.

 

[TchrWill]

The formula for calculating a monthly loan payment is R = Pi/[1 - 1/(1+i)^n] where R = the periodic payment, P = the principal, or debt to be paid off, n = the number of payment periods over which the payments will take place, and i = the periodic interest rate in decimal form. The interest rate for a loan is usually quoted as an annual rate such as 8%. In the formula the first thing we do is convert this to i = .08 when considering annual payments.
If payments are to be made monthly, i = .08/12 = .006666 as the monthly interest rate. An example will illustrate the use of the formula.
Lets say you want to borrow $10,000 for a home improvement, to be paid off monthly over a period of 5 years, with an annual interest rate of 8%. So P = 10,000, n = 5 x 12 = 60, i = .08/12 = .006666. Then we have R = 10000(.006666)/[1 - 1/(1+.006666)^60] = 66.66/[1 - 1/(1.489790] = 66.66/.328764 = $202.76 per month. As simple as that. Over the life of the loan you will pay $12,165.49 back to the bank thereby incurring the cost of $2,165.49 for the priviledge of borrowing the money.

You need only plug in your knowns and solve for the imterest rate.

 

[gmblng]

Thank you, but I am still confused. It looks like there are 2 places where I need an "i" - the top of the equation and the bottom. I don't know how to solve if I have to times the principal by the interest rate wince I don't know what it is yet!

Principal = 85,000
periodic payment = $8,273.29 a year
n = 30 years or 360 payments
i = ?

I follow your example and can do it on my calculator, but you have the interest rate in there - could you please show me an example without it?

Thanks so much for your help!

 

[tkhunny]

Good news! Your efforts have not been in vain. It CANNOT be solved. Numeric, iterative techniques must be used to find it. Have you ever noticed that your calculator takes WAY longer to solve for 'i' than it does for any of the other missing parts? There is no direct solution using functions with which you are familiar.

 

[Denis]

Thank you, but I am still confused. It looks like there are 2 places where I need an "i" - the top of the equation and the bottom. I don't know how to solve if I have to times the principal by the interest rate wince I don't know what it is yet!
Principal = 85,000
periodic payment = $8,273.29 a year
n = 30 years or 360 payments
i = ?
I follow your example and can do it on my calculator, but you have the interest rate in there - could you please show me an example without it?
Thanks so much for your help!

Your example is unclear: if the PERIODIC payment is 8273.29 yearly,
then n = 30, NOT 360; you are borrowing 85000.00 and paying it back
with ANNUAL payments of 8273.29; the interest rate will be 9% compounded
ANNUALLY, and (as TK told you) can only be calculated by iteration
(fancy word for guess work!).

My way to "find" the rate in these cases:
1: try a (as reasonable as possible) rate and see what payment results
2: if payment higher, then rate too high, so reduce gradually
3: if payment lower, then rate too low, so increase gradually