# How to calculate the interest rate ?

#### GregoryQueen

##### New member
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
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:

#### GregoryQueen

##### New member
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:

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.

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#### tkhunny

##### Moderator
Staff member
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:

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

#### JeffM

##### Elite Member
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
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
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
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)

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
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
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
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.

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#### JeffM

##### Elite Member
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
Beer soaked ramblings follow.
From which calculation do you get this interest?
I mean 0,0045833023239915

#### jonah2.0

##### Full Member
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
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
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
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.
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
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