# Need some help understanding Rate function

Copper Contributor

# Need some help understanding Rate function

Hi, I need some help to understand how Rate function works in this case :I want to calculate APR of one year of the loan. Let's say the loan is 1000000 for the period of 4 years and annual fees and interests are 100865. If I would calculate simply just dividing 100865/1000000, I would get 10.09 %. That's my desired outcome.
As I understand Rate function, you need a number of periods - nper , payments - pmt and present value - pv.  Inputing my values into Rate function :
nper:  4

pmt: -100865
pv: 1000000
At this point my reasoning is : I have 4 periods with annual payment of 100865  to the loan, but Rate function gives me -28,49 %:  Whats going on here? Why does it give a negative percentage? If I would change nper argument to 1 I would get -89,91 % and if I would add 1 to this result, I would get my desired outcome. Is this correct calculation to get APR at this point? Or what I am getting?

6 Replies

# Re: Need some help understanding Rate function

@GediminasC  wrote:  ``annual fees and interests are 100865 [....] pmt: -100865``

You get a negative rate because 4 payments of 100865 = 403460 is not enough to pay off a loan of 1000000, not to mention interest and additional fees.

Excel financial functions like RATE assume a declining principal balance with each payment.  Therefore, the amount of interest also declines with each payment.

We cannot say anything about the periodic fees because you did not.

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@GediminasC  wrote:  ``If I would calculate simply just dividing 100865/1000000, I would get 10.09 %. That's my desired outcome``

If 10.0865% is the desired annual rate for fees and interest, the minimum payment is 316061.71; namely:

=-PMT(10.0865%, 4, 1000000)

Then, the loan is amortized with annual payments over 4 years as follows.

Formulas:

B5: =\$A\$1

C5: =B5-D5

D5: =E4*10.0865%

E5: =E4+D5-B5

# Re: Need some help understanding Rate function

Fees and interest are based on percentage of principal. So i would say its fees and interest are the same. In this case it would be 100865,

Hm, i was assuming that I only need fees and interest as payment (pmt) and the function would divide principal into 4 periodic payments and would add it to interest and fees. Ok, thats error of mine.
If I say now that mine annual payment is : fees and interest 100865 + principal part 250000
my arguments
nper: 4
pmt: -350865
pv: 1000000
Rate would be = 15,08%
Hm, the APR formula that i have is
(Fees + Interest/Principal)/n*365*100
where:
Interest = total interest paid
Principal = Loan amount
n =is the number of days in loan term
So if put values in it :
((100865 * 4 ) / 1000000 / 1460 (four years in days) * 365 *100 = 10,0865 %
So now i dont get what percentage of rate function represents with 15,08%

# Re: Need some help understanding Rate function

@GediminasC  wrote:  ``the APR formula that i have is (Fees + Interest/Principal)/n*365*100``

Loans can be structured in a lot of different ways, and "APR" can be calculated in a lot of different ways, both subject to local laws.

The methods that you described are not consistent with the methods that Excel financial functions, notably RATE, are based on.

(Excel financial functions use the so-called actuarial method.  In contrast, are you following Islamic banking practices?)

So, if you continue to use different methods, you should abandon your use of the RATE function.  GIGO! ("Garbage in, garbage out")

That said, I cannot tell if you truly understand your loan methods, or if you simply misunderstand them.

So, I really cannot help you further.

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I will comment on some inconsistencies in your mathematics, as you present them.

First, you seem to have a typo in your abstract definition of APR.  In part, you are calculating:

(fees + interest) / principal

not

(fees + interest/principal)

I believe the first expression is correct, if 100865 is fees+interest.

Second, when you multiply by 100 at the end, the result is the decimal number 10.0865, not the percentage 10.0865% as you wrote.

(Note that I use period as the decimal point, whereas you use comma.  That is not an issue.)

In fact, I deprecate the practice of multiplying by 100 at the end.  I know that it is common practice in some presentation of "percentages".  But it just confuses calculations, as you demonstrate.

# Re: Need some help understanding Rate function

The issue you are encountering with the RATE function is related to the sign convention used in financial functions. The RATE function assumes that cash outflows (payments made) are represented by negative numbers, and cash inflows (receipts or money received) are positive.

In your case, you are dealing with a loan, which means you are making payments to pay off the loan, so the payment should be represented as a negative number.

Let's correct your inputs:

• NPER: Number of periods, which is 4 (for 4 years).
• PMT: Payment made each period, which is the annual payment to the loan. Since it's an outgoing payment, it should be represented as a negative number. So, PMT should be -100865.
• PV: Present value, which is the loan amount. Since it's an outgoing payment (you are receiving the loan amount), it should be represented as a positive number. So, PV should be 1000000.

Now, using the corrected inputs:

=NOMINAL(RATE(4, -100865, 1000000), 1)

Note:

1. The RATE function returns the periodic interest rate. To convert it to an annual rate, you can use the NOMINAL function.
2. The NOMINAL function takes the periodic interest rate and the number of compounding periods per year (1 for annual compounding) and returns the nominal annual interest rate.

By doing this, you should get the desired APR. The negative sign in the result simply indicates that it's an outgoing payment (cash outflow) according to the sign convention used in financial functions. AI was partially deployed to support the text.

My answers are voluntary and without guarantee!

Hope this will help you.

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# Re: Need some help understanding Rate function

It's always amazing that people only become happy when they make stupid comments about others. Everyone tries to help everyone here, the fact that it doesn't always work doesn't mean that no one should get in touch because someone makes another stupid comment. I pay very close attention to such understated comments that refer to any person.

In order not to be misunderstood,

I am always happy to receive constructive and detailed feedback and corrections.

Apparently there was a misunderstanding in my first answer, which has now been clarified.