How to calculate the interest rate ?

GregoryQueen

New member
Joined
Mar 29, 2021
Messages
7
The bank gave us a loan of 75,000 for 30 years. We pay 425.84 per month. How to calculate the interest rate per year? Please, give me advice and formula, Thank you.
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
24,338
The bank gave us a loan of 75,000 for 30 years. We pay 425.84 per month. How to calculate the interest rate per year? Please, give me advice and formula, Thank you.
Do you know the equation used for calculating monthly payments for a given loan amount, interest rate and loan-duration?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 

GregoryQueen

New member
Joined
Mar 29, 2021
Messages
7
Do you know the equation used for calculating monthly payments for a given loan amount, interest rate and loan-duration?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
I don't know the equation that can calculate the annual interest rate. I tried different ways but it always came out wrong. I don't know the equation that can calculate the annual interest rate.
 
Last edited:

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
11,307
There isn't an equation to "calculate" the interest rate. You must go hunting for it. There are numerical methods that will help you on your way. You can write an expression for all the other pieces to be easily calculated individually. You CANNOT write such an expression for the interest rate.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about this problem.

Banks are required to give disclosures for this sort of thing. Please go back and READ the terms of your loan.
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
6,315
There is no true formula, but excel has a so-called formula that will estimate the answer.

Also, in the U.S., the interest rate must be disclosed so you never have any need to compute it.
 

GregoryQueen

New member
Joined
Mar 29, 2021
Messages
7
Do you want me to show you my miscalculation here?

The result of this calculation is 5.5% per year, but I don't know how to calculate it.
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
6,315
Do you want me to show you my miscalculation here?

The result of this calculation is 5.5% per year, but I don't know how to calculate it.
Well you certainly can validate or invalidate it.
 

GregoryQueen

New member
Joined
Mar 29, 2021
Messages
7
Formula for interest:
I = RC - C
where:
I - Interest
RC - Repaid Credit (153 302,4)
C - Credit (75 000)

I = 153 302,4 - 75 000; I = 78 302,4
153 302,4 because 425,84 * 360 (12 months * 30 years)


Formula for Rate of return:
RoR = Interest / Credit
RoR = 78 302,4 / 75 000 = 1,044032


Formula for Nominal Interest Rate:
NIR = Rate of return / period
NIR = 1,044032 / 1 = 1,044032 = 104,40% (WRONG RESULT)


Correct answer is 5,5%
According to the formula for Rate of return, we should have:
79 125 - 75 000 / 75 000 = 4125 / 75 000 = 0,055 = 5,5%

i have no idea where the number 79 125 came from.
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
6,315
You are mixing up simple interest and compound interest. There is no formula for what you are looking for. This is the third time you have been told: THERE IS NO FORMULA.
 

GregoryQueen

New member
Joined
Mar 29, 2021
Messages
7
I don't have problem doing this in excel or calculator.

You mean the formula for calculating this exercise doesn't exist?
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
24,338
I don't have problem doing this in excel or calculator.

You mean the formula for calculating this exercise doesn't exist?
There is no CLOSED FORM equation. It is solved through iterative method.
 

jonah2.0

Full Member
Joined
Apr 29, 2014
Messages
385
Beer soaked ramblings follow.
I don't have problem doing this in excel or calculator.

You mean the formula for calculating this exercise doesn't exist?
That is correct laddie.

20210402_194842.jpg
Screenshot_20210402-192951_991EX.jpg
 
Last edited:

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
6,315
I don't have problem doing this in excel or calculator.

You mean the formula for calculating this exercise doesn't exist?
I told you in post 5 that excel could approximate it. I also said that excel used a “so called” formula. It is not a closed form formula; it invokes an iterative algorithm
 

GregoryQueen

New member
Joined
Mar 29, 2021
Messages
7

jonah2.0

Full Member
Joined
Apr 29, 2014
Messages
385
Beer soaked ramblings follow.
From which calculation do you get this interest?
I mean 0,0045833023239915
Did you not notice the first excel screenshot where I highlighted the “so called” formula format that JeffM intimated at post #13. The 2nd screenshot was merely for show to let you know that you are to plug the value of x into the amortization expression to assure yourself that you will get the loan amount should you do so.
 

GregoryQueen

New member
Joined
Mar 29, 2021
Messages
7
Beer soaked ramblings follow.

Did you not notice the first excel screenshot where I highlighted the “so called” formula format that JeffM intimated at post #13. The 2nd screenshot was merely for show to let you know that you are to plug the value of x into the amortization expression to assure yourself that you will get the loan amount should you do so.
So, interest in Excel is calculated automatically? Don't you know how to calculate them?
I seem in the first first screenshot you highlighted the result from second screenshot.
If the "x" in the second screenshot is interest rate (which I'm looking for), then I don't need interest which is "i" in the fist screenshot.
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
6,315
So, interest in Excel is calculated automatically? Don't you know how to calculate them?
I seem in the first first screenshot you highlighted the result from second screenshot.
If the "x" in the second screenshot is interest rate (which I'm looking for), then I don't need interest which is "i" in the fist screenshot.
Things like the interest rate implied by the amount of the periodic payment, the original principal,and the number of periodic payments are not calculated by a formula as you understand it. They can be APPROXIMATED by something called a numerical method or iterative process, which are sophisticated versions of trial and error. They are a royal pain in the ass to do by hand, but computers do them readily.

I have no idea which one is used by Excel for calculating interest on annuities. Because Excel asks for a single initial guess, it may be using the Newton-Raphson method, which requires an initial guess.

If you remember your calculus, you can look up the Newton-Raphson method on google.

For an example of a different method of an iterated process, l shall show you the bisection method for finding an approximation to the square root of two.

\(\displaystyle 1 < 2 < 4 \implies 1 < \sqrt{2} < 2.\)

\(\displaystyle \left ( \dfrac{1 + 2}{2} \right )^2 = 1.5^2 2.25 > 2 \implies 1 < \sqrt{2} < 1.5.\)

\(\displaystyle \left ( \dfrac{1 + 1.5}{2} \right )^2 = 1.25^2 = 1.5625 < 2 \implies 1.25 < \sqrt{2} < 1.5.\)

\(\displaystyle \left ( \dfrac{1.25 + 1.5}{2} \right )^2 = 1.375^2 = 1.890625 < 2 \implies 1.375 < \sqrt{2} < 1.5.\)

\(\displaystyle \left ( \dfrac{1.375 + 1.5}{2} \right )^2 = 1.4375^2 = 2.06640625 > 2 \implies 1.375 < \sqrt{2} < 1.4375.\)

You keep doing that until you get a good enough approximation. It should be intuitive already that the answer will be close to 1.4.

You will get a good approximation doing that, but it is not a simple formula. Computers can do it quickly without error.
 

jonah2.0

Full Member
Joined
Apr 29, 2014
Messages
385
Beer soaked ramblings and sarcasm follows.
So, interest in Excel is calculated automatically? Don't you know how to calculate them?
Don't you read what volunteer helpers here are trying to tell you?
What're you blind?
I seem in the first first screenshot you highlighted the result from second screenshot.
Mind your grammar.
If the "x" in the second screenshot is interest rate (which I'm looking for), then I don't need interest which is "i" in the fist screenshot.
The nominal rate compounded monthly is `j` (1st screenshot) and `i` (1st screenshot) is the effective monthly rate (x in the 2nd screenshot). How would you know how much interest you'll pay per month on the outstanding balance of your loan if you don't know what `i` is?
 

Kenaida

New member
Joined
Apr 5, 2021
Messages
4
The bank gave us a loan of 75,000 for 30 years. We pay 425.84 per month. How to calculate the interest rate per year? Please, give me advice and formula, Thank you.
Hi if you want a quick and simple answer in Excel just use this formula

=RATE(30*12,-425.84,75000,0)*12

1) make sure the payments are negative.
2) the zero at the end is that you want to assume the balance is reduced to zero at the end of term

3) To improve accuracy, it matters slightly if you are charged interest at the beginning of the month or at the end.

Charged at the end of each month : =RATE(30*12,-425.84,75000,0,0)*12

Charged at the start of each month : =RATE(30*12,-425.84,75000,0,1)*12
 
Top