Credit Card Interest Calculation: loan w/ 0% interest, but handling fee

taraK

New member
Joined
Jun 12, 2018
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Where I live there are a lot of credit cards that offer a loan of money and charge a handling fee, but then offer a 0% interest charge for the period of the loan. The loan is often 12 - 36 months in length, but unlike some loans, requires some payment each month. This amount varies but is usually around 2.5-5% of the outstanding balance. At the end of the load period the remaining balance would either have to be repaid in full or have a huge (typical credit card) interest rate placed on the balance -- typically around 29% per year.

Question -- how to work out the actual interest rate of one of these loans -- assuming that the whole balance is then paid off in the last month so no additional interest is paid?

Example:
Loan $7,000
Handling Fee: 3% (ie, $210)
Interest per month on loan: 0%
Pay back each month: 5% of balance
Loan Term: 24 month.


Month No.Balanceinterest this monthpay back this monthcarry
0
7,210.000
0.000
360.500
6,849.500
1
6,849.500
0.000
342.475
6,507.025
2
6,507.025
0.000
325.351
6,181.674

22
2,332.677
0.000
116.634
2,216.043
23
2,216.043
0.000
110.802
2,105.241
24
2,105.241
0.000
105.262
1,999.979

--So about $2,000 has to be paid back at month 24. But what is the effective interest of this loan?
 
Where I live there are a lot of credit cards that offer a loan of money and charge a handling fee, but then offer a 0% interest charge for the period of the loan. The loan is often 12 - 36 months in length, but unlike some loans, requires some payment each month. This amount varies but is usually around 2.5-5% of the outstanding balance. At the end of the load period the remaining balance would either have to be repaid in full or have a huge (typical credit card) interest rate placed on the balance -- typically around 29% per year.

Question -- how to work out the actual interest rate of one of these loans -- assuming that the whole balance is then paid off in the last month so no additional interest is paid?

Example:
Loan $7,000
Handling Fee: 3% (ie, $210)
Interest per month on loan: 0%
Pay back each month: 5% of balance
Loan Term: 24 month.


Month No.Balanceinterest this monthpay back this monthcarry
0
7,210.000
0.000
360.500
6,849.500
1
6,849.500
0.000
342.475
6,507.025
2
6,507.025
0.000
325.351
6,181.674

22
2,332.677
0.000
116.634
2,216.043
23
2,216.043
0.000
110.802
2,105.241
24
2,105.241
0.000
105.262
1,999.979

--So about $2,000 has to be paid back at month 24. But what is the effective interest of this loan?
Not enough information.

1) 8/100 = 0.080 Effective in Arrears
2) 8/(100-8) = 0.087 Effective in Advance

"handling fee and no interest" is generally just false. You're paying interest in advance.
 
Where I live there are a lot of credit cards that offer a loan of money and charge a handling fee, but then offer a 0% interest charge for the period of the loan. The loan is often 12 - 36 months in length, but unlike some loans, requires some payment each month. This amount varies but is usually around 2.5-5% of the outstanding balance. At the end of the load period the remaining balance would either have to be repaid in full or have a huge (typical credit card) interest rate placed on the balance -- typically around 29% per year.

Question -- how to work out the actual interest rate of one of these loans -- assuming that the whole balance is then paid off in the last month so no additional interest is paid?

Example:
Loan $7,000
Handling Fee: 3% (ie, $210)
Interest per month on loan: 0%
Pay back each month: 5% of balance
Loan Term: 24 month.


Month No.Balanceinterest this monthpay back this monthcarry
0
7,210.000
0.000
360.500
6,849.500
1
6,849.500
0.000
342.475
6,507.025
2
6,507.025
0.000
325.351
6,181.674

22
2,332.677
0.000
116.634
2,216.043
23
2,216.043
0.000
110.802
2,105.241
24
2,105.241
0.000
105.262
1,999.979

--So about $2,000 has to be paid back at month 24. But what is the effective interest of this loan?
There is no additional interest paid back since the interest rate is 0%, meaning you paid no interest back for the loan period. I guess you want to include the handling fee as interest, as I would do. The problem is that you are not giving us the exact % you are paying back per month. Do you want the interest rate compounded yearly, quarterly or continuous?
I would use simple interest and just divide the 3% fee by the two years and say that the yearly interest rate is 1.5%/year
 
No way Ozay...apply 1.5% to the resulting monthly balances
and you'll get approx. 130, quite far from the actual 210.
Yeah, you are taking into account that their balance is decreasing. Since there is no interest I admit that I ignored that. The bottom line is that they borrowed say $7000 and in the end paid back 3% over that. I understand that they did not borrow all of the $7000 for two years as they paid back some before the two years expired.
 
Not enough information.

1) 8/100 = 0.080 Effective in Arrears
2) 8/(100-8) = 0.087 Effective in Advance

"handling fee and no interest" is generally just false. You're paying interest in advance.

Hi, What additional information do you want? Yes I agree, the handling fee is just an advance interest charge, in effect; but with the changing balance each month what is the equivalent rate ? I mean, it would be interesting to compare this type of loan with say one where you are borrowing $3,000 at 3% over a similar period (etc). Which one(s) is/are better value; is there a generic algorithm to work it out?
 
Is this same as yours:
Code:
MONTH    PAYMENT   BALANCE
   0               7210.00
   1     360.50    6849.50
   2     342.48    6507.02
   3     325.35    6181.67
.....
  22     122.77    2332.68
  23     116.63    2216.05
  24    2216.05        .00


Yes this is the same -- I just put the payment at month zero
 
There is no additional interest paid back since the interest rate is 0%, meaning you paid no interest back for the loan period. I guess you want to include the handling fee as interest, as I would do. The problem is that you are not giving us the exact % you are paying back per month. Do you want the interest rate compounded yearly, quarterly or continuous?
I would use simple interest and just divide the 3% fee by the two years and say that the yearly interest rate is 1.5%/year

1. In the example I gave I decided on a 5% payback. The only reason I mentioned a range before to give some background information.
2. It would be nice to have a continuous, compound interest, but I left that up to anyone who might reply.
3. The trouble with 1.5% as an answer is that it's not a fixed balance -- it's reducing each month so the effective interest rate is increasing. I would like to be able to compare various "loans" -- for example, to compare loans ones like this one; to loans that charge a percent each month on the outstanding balance (a mortgage type loan); to a bank saving account, where the interest is paid on the deposit.
 
Question -- how to work out the actual interest rate of one of these loans -- assuming that the whole balance is then paid off in the last month so no additional interest is paid?

Therein lies the problem. The "actual interest rate" is whatever is in the plan documents and disclosed by the lender. If you mean, the equivalent interest rate using some familiar method, then that is a different question and that is mostly what has been discussed in this thread. The fact that different methods produce different results does NOT make one of the methods anything that isn't "actual".

Note: If is a credit card, it's unlikely to use equally-sized months.
 
Last edited:
Here's a fun variation.





Balance
Interest
Payment
0
7,210.00
14.56
1
6,863.33
13.86
361.23
2
6,533.33
13.19
343.86
3
6,219.20
12.56
327.33
4
5,920.17
11.95
311.59
5
5,635.52
11.38
296.61
6
5,364.55
10.83
282.34
7
5,106.61
10.31
268.77
8
4,861.08
9.82
255.85
9
4,627.35
9.34
243.54
10
4,404.86
8.89
231.83
11
4,193.07
8.47
220.69
12
3,991.46
8.06
210.08
13
3,799.54
7.67
199.98
14
3,616.85
7.30
190.36
15
3,442.95
6.95
181.21
16
3,277.41
6.62
172.50
17
3,119.82
6.30
164.20
18
2,969.82
6.00
156.31
19
2,827.02
5.71
148.79
20
2,691.10
5.43
141.64
21
2,561.70
5.17
134.83
22
2,438.53
4.92
128.34
23
2,321.28
4.69
122.17
24
2,209.67
116.30

You can enjoy figuring out what I did. Hint: The lender is a liar. There really is interest, but they are making you pay it up front, and then financing it for you, so they can charge even more interest on that!

This produces a nominal annual interest rate of 2.4232%, Effective: 2.4503%.

Note: This is also why your monthly statement says something like, "This is not the payoff value. You have to call us for that."
 
Who cares: I ended up with rate ~2.42 as you did...

Plus a $7000 loan costing only $210 over 2 years
is a good deal no matter how you cook it!!
I'd take it and lend it to Jomo at 22%....


So, thanks to you all who have suggested a rate, but how did you work it out !?
That is, if I were to choose another card it might have different initial conditions,
for example:
Loan: $7000
payback per month: 4%
term: 36 months
handling fee: 3.29%
interest per month:0%
 
So, thanks to you all who have suggested a rate, but how did you work it out !?
That is, if I were to choose another card it might have different initial conditions,
for example:
Loan: $7000
payback per month: 4%
term: 36 months
handling fee: 3.29%
interest per month:0%

I don't claim to know the details of finance, but I made a spreadsheet using what makes sense to me (from the original scenario, but assuming the first payment is made after one month, and the last payment covers the entire balance). Then I used Excel's Goal Seek feature to find the interest rate at which, if a loan of $7000 were made with the same payments, the total interest paid would be $210. This turned out to be 2.66%.

FMH111457.jpg

For taraK's new scenario, I get 2.09%.

It is conceivable that a formula could be worked out using some sort of series, but that doesn't seem worth it when a spreadsheet can do it easily.

Others will have to determine whether what I have done makes sense financially.
 
I don't claim to know the details of finance, but I made a spreadsheet using what makes sense to me (from the original scenario, but assuming the first payment is made after one month, and the last payment covers the entire balance). Then I used Excel's Goal Seek feature to find the interest rate at which, if a loan of $7000 were made with the same payments, the total interest paid would be $210. This turned out to be 2.66%.

View attachment 9643

For taraK's new scenario, I get 2.09%.

It is conceivable that a formula could be worked out using some sort of series, but that doesn't seem worth it when a spreadsheet can do it easily.

Others will have to determine whether what I have done makes sense financially.
Was having another look at this "loan thing".
Borrower borrows 7000; pays 210 right away as fee:
so has use of 6790 (BALANCE1 below)
Lender will put this 210 in "revenue", and book a 7000 loan (BALANCE2 below).
So, doing the "work" similarly to Dr.P will result in this "picture":
Code:
MONTH  PAYMENT  INTEREST   BALANCE1  BALANCE2
  0                        6790.00   7000.00
  1     350.00     14.70   6454.70   6650.00
  2     332.50     13.97   6136.17   6317.50
  3     315.87     13.28   5833.58   6001.63
....
 22     119.20      5.13   2255.20   2264.74
 23     113.24      4.88   2146.83   2151.50
 24    2151.50      4.67       .00       .00
                  ------
                  210.00
Results in 2.598% APR cpd. monthly, which is 2.629% effective.
Purty close to your 2.66% DrP!
 
So, thanks to you all who have suggested a rate, but how did you work it out !?
That is, if I were to choose another card it might have different initial conditions,
for example:
Loan: $7000
payback per month: 4%
term: 36 months
handling fee: 3.29%
interest per month:0%

1) This all is insufficiently defined. You need MUCH better information.
2) There are infinitely many ways to proceed. Maybe only a couple thousand reasonable ways.
3) There are many tools to help you on your way. MS Excel is one.
 
Was having another look at this "loan thing".
Borrower borrows 7000; pays 210 right away as fee:
so has use of 6790 (BALANCE1 below)
Lender will put this 210 in "revenue", and book a 7000 loan (BALANCE2 below).
So, doing the "work" similarly to Dr.P will result in this "picture":
Code:
MONTH  PAYMENT  INTEREST   BALANCE1  BALANCE2
  0                        6790.00   7000.00
  1     350.00     14.70   6454.70   6650.00
  2     332.50     13.97   6136.17   6317.50
  3     315.87     13.28   5833.58   6001.63
....
 22     119.20      5.13   2255.20   2264.74
 23     113.24      4.88   2146.83   2151.50
 24    2151.50      4.67       .00       .00
                  ------
                  210.00
Results in 2.598% APR cpd. monthly, which is 2.629% effective.
Purty close to your 2.66% DrP!

Thanks for the replies.
--In fact the lender adds on the handling fee to the bill at the end of the month. So they, the credit card company, will send you your loan amount (in your example that $7000) but your statement from the said credit card company in month one will show a balance of $7210 that needs repaying and a minimum payment amount at 5% of outstanding balance that is $360.50 to be paid.
How did you goal seek on a range of months? I don't see how you are proportioning the "interest" across the 24 odd months to get the total to be $210?
 
1) This all is insufficiently defined. You need MUCH better information.
2) There are infinitely many ways to proceed. Maybe only a couple thousand reasonable ways.
3) There are many tools to help you on your way. MS Excel is one.

What more information do you need? This is a true life example, it isn't a made up scenario.
 
Thanks for the replies.
--In fact the lender adds on the handling fee to the bill at the end of the month. So they, the credit card company, will send you your loan amount (in your example that $7000) but your statement from the said credit card company in month one will show a balance of $7210 that needs repaying and a minimum payment amount at 5% of outstanding balance that is $360.50 to be paid.
How did you goal seek on a range of months? I don't see how you are proportioning the "interest" across the 24 odd months to get the total to be $210?

If you can confirm or correct the numbers in the first three columns of my spreadsheet, I can tell you how I did the rest, which I think is the best answer we have found for your question. But I made the goal the total interest, in the fifth column, being 210, by manipulating the interest rate at top right. The idea is to suppose that interest is being charged on the outstanding balance each month from the lender's perspective, while the payments are based on the outstanding balance from the borrower's perspective.
 
What more information do you need? This is a true life example, it isn't a made up scenario.
The EXACT methodology. Your disclosures do not contain it all. It is unlikely that you can confirm or deny ANY of the examples that have been provided. We're just guessing until EXACT information is given. We may need payment dates and average balances. Who knows?!
 
Well, if that's the case, then my previous post changes slightly to:

Borrower borrows $7000; pays back $7210 over 24 months.:
so has use of $7000 (BALANCE1 below)
Lender will book a $7210 loan (BALANCE2 below).
So, using brute strength method ("seek" or whatever...)
Code:
MONTH  PAYMENT  INTEREST   BALANCE1  BALANCE2
  0                        7000.00   7210.00
  1     360.50     14.71   6654.21   6649.50
  2     342.47     13.98   6365.72   6507.03
  3     325.35     13.28   6013.65   6181.67
....
 22     122.77      5.13   2323.15   2332.68
 23     116.63      4.88   2211.40   2216.05
 24    2216.05      4.65       .00       .00
                  ------
                  210.00
Results in monthly rate of .00210075, or .0255023 effective, so ~2.55%.

I differ slightly from DrP's method since I have some interest at 24th payment.

PLUS I'll repeat that the ONLY way to solve directly is
using the average balance owing....
 
Well, if that's the case, then my previous post changes slightly to:

Borrower borrows $7000; pays back $7210 over 24 months.:
so has use of $7000 (BALANCE1 below)
Lender will book a $7210 loan (BALANCE2 below).
So, using brute strength method ("seek" or whatever...)
Code:
MONTH  PAYMENT  INTEREST   BALANCE1  BALANCE2
  0                        7000.00   7210.00
  1     360.50     14.71   6654.21   6649.50
  2     342.47     13.98   6365.72   6507.03
  3     325.35     13.28   6013.65   6181.67
....
 22     122.77      5.13   2323.15   2332.68
 23     116.63      4.88   2211.40   2216.05
 24    2216.05      4.65       .00       .00
                  ------
                  210.00
Results in monthly rate of .00210075, or .0255023 effective, so ~2.55%.

I differ slightly from DrP's method since I have some interest at 24th payment.

PLUS I'll repeat that the ONLY way to solve directly is
using the average balance owing....

Comparing my spreadsheet with your data, I realized I was using the wrong balance for the interest calculation. Fixing that gives me more or less the same numbers, with a rate of 2.52% (nominal annual rate) from Goal Seek:

FMH111457 fixed.jpg
 
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