How to calculate a fixed rate of interest on a Balloon Payment loan

nicoprz

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Sep 20, 2018
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Hi, I am a software developer creating a loan repayments calculator. With this calculator the known values are the initial cost, a balloon payment at the end and the APR; using these I have been able to write a script which calculates the monthly repayment.

For legal reasons I need to be able to show the fixed rate of interest for this period, however I can't figure out how to find that. Using a standard calculation for this doesn't work sadly.

This is the example I have been provided with:

Loan Value: £12000
APR: 7.9%
24 Monthly Payments Of: £194.58
1 Final Payment: £9000
Duration of agreement: 24months + 1
Interest Rate: 4.07%
Total Amount Payable: £16,669.92

If anyone is able to ascertain how the interest rate of 4.07% is calculated then I would really appreciate it

Thanks :D
 
Hi, I am a software developer creating a loan repayments calculator. With this calculator the known values are the initial cost, a balloon payment at the end and the APR; using these I have been able to write a script which calculates the monthly repayment.

For legal reasons I need to be able to show the fixed rate of interest for this period, however I can't figure out how to find that. Using a standard calculation for this doesn't work sadly.

This is the example I have been provided with:

Loan Value: £12000
APR: 7.9%
24 Monthly Payments Of: £194.58
1 Final Payment: £9000
Duration of agreement: 24months + 1
Interest Rate: 4.07%
Total Amount Payable: £16,669.92

If anyone is able to ascertain how the interest rate of 4.07% is calculated then I would really appreciate it

Thanks :D
How have you calculated the total amount payable? 24*194.58 +9000 = 13669.92 not 16669.92?
 
Hi, I am a software developer creating a loan repayments calculator. With this calculator the known values are the initial cost, a balloon payment at the end and the APR; using these I have been able to write a script which calculates the monthly repayment.

For legal reasons I need to be able to show the fixed rate of interest for this period, however I can't figure out how to find that. Using a standard calculation for this doesn't work sadly.

This is the example I have been provided with:

Loan Value: £12000
APR: 7.9%
24 Monthly Payments Of: £194.58
1 Final Payment: £9000
Duration of agreement: 24months + 1
Interest Rate: 4.07%
Total Amount Payable: £16,669.92

If anyone is able to ascertain how the interest rate of 4.07% is calculated then I would really appreciate it

Thanks :D

The real question is, what is it that you are trying to do? Why would the "Interest Rate" be substantially different from the "APR"? That makes no sense. Is the APR variable? Is the Lump at a different APR.

Solving for an interest rate with a complicated payment stream often requires iterative techniques.
 
The real question is, what is it that you are trying to do? Why would the "Interest Rate" be substantially different from the "APR"? That makes no sense. Is the APR variable? Is the Lump at a different APR.

Solving for an interest rate with a complicated payment stream often requires iterative techniques.
I think the "interest rate" is the "effective interest rate" which is a legal requirement so that loans can be compared. Am I right nicoprz?
 
The rate used is 7.9% EFFECTIVE annual, meaning ~.635634% monthly.
The 4.07% that you show seems to pop out of the blue!
WHY d'heck are you showing it?

Here's what it looks like in bank statement format:

Code:
MONTH  PAYMENT  INTEREST      BALANCE
   0                         12000.00
   1   -194.58    76.28      11881.70 : 12000*.00635634 = 76.28
   2   -194.58    75.52      11762.64
.....
  23   -194.58    58.58       9080.03
  24   -194.58    57.70       8943.15
  25  -9000.00    56.85           .00
PROPERLY worded, the problem should be along the lines of:
A loan of $12,000.00 is repayable at 24 monthly payments of $194.58
and a 25th balloon payment of $9,000.00.
What is the annual effective rate?
 
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I think the "interest rate" is the "effective interest rate" which is a legal requirement so that loans can be compared. Am I right nicoprz?

This is correct.

The rate used is 7.9% EFFECTIVE annual, meaning ~.635634% monthly.
The 4.07% that you show seems to pop out of the blue!
WHY d'heck are you showing it?

I have to show this for the legal requirement. It does seem to pop out of the blue, but it will be correct :)

Some background on this: I am a web developer and I am making a calculator for a loan company to use on several car manufacturer websites. One of the manufacturers have a requirement of using a balloon payment loan, where the balloon is based off a percentage of the vehicle value. In this case the balloon payment is 60% of the vehicle cost. These quotes aren't legally binding however they are required to show a representative APR and a fixed rate of interest.
 
Some background on this: I am a web developer and I am making a calculator for a loan company to use on several car manufacturer websites. One of the manufacturers have a requirement of using a balloon payment loan, where the balloon is based off a percentage of the vehicle value. In this case the balloon payment is 60% of the vehicle cost. These quotes aren't legally binding however they are required to show a representative APR and a fixed rate of interest.
You've already told us most of this...

If you do not understand what I showed you in the "bank statement", then....

That mysterious "4.07%" is still a mystery...
can you not at least SHOW where it comes from?

The balloon pay't being 60% of cost is easy to see:
.60c = 9000 : c = 15000
Then loan = 12000 (after the 3000 down payment)

Once more: explain the 4.07%, else we can't help...
 
You've already told us most of this...

If you do not understand what I showed you in the "bank statement", then....

That mysterious "4.07%" is still a mystery...
can you not at least SHOW where it comes from?

The balloon pay't being 60% of cost is easy to see:
.60c = 9000 : c = 15000
Then loan = 12000 (after the 3000 down payment)

Once more: explain the 4.07%, else we can't help...


I understand the bank statement, the balloon and the payments just fine. I can’t tell you how to get to 4.07, this is the entire reason I am here: to try and find out how this number is derived.
 
I understand the bank statement, the balloon and the payments just fine. I can’t tell you how to get to 4.07, this is the entire reason I am here: to try and find out how this number is derived.
Wish you has stated this right off the bat!

If you don't know where this 4.07 comes from or what it represents,
then it's impossible to do anything...
A bit like: I bought 12 apples for $6.00, sales tax 10%
My receipt has an extra line showing 2.5%: explain it !!
At least I can ask the sales clerk/cashier;
can't you ask anyone?
 
… the entire reason I am here: to try and find out how this number is derived …
It seems like you've fixed your cart in front of somebody else's horse.

That is, there's a world of difference between asking for help using an established formula or algorithm and asking for help understanding how a numerical value results (a value that you already knew to be peculiar) from a process described by only a single, concise example. We've told you more than once that 4.07% is not related (in any basic way) to the remaining information, as posted.


… [4.07%] will be correct …
Please explain how you know this. It can't be from first-hand research because you don't have a meaning for "Interest Rate" that jives 0.0407 with the rest of what you've posted.

Somebody gave you this example. Ask the source to double-check their numbers; maybe there's one or more typos. Otherwise, they're doing something that's not "mainstream". :cool:
 
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Was this 3000 deposit made one month after the loan or at the time of the loan?
Can you please answer this question. Then maybe I can help.
Edit: Is the 3000 the down payment? So the car is 15000, but you are borrowing 12000.
 
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I assumed the 7.9% was compound. We're trying to find the effective rate aren't we??
Well, the 194.58 is a GIVEN in the problem (see 1st post).
What I did was determine the monthly cpd. rate that results
in the payment of 194.28
 
Hi guys, sorry for not replying for a few days, my wife had a baby so have been a little bit busy. Thanks so far for everyone's help. I understand the interest rate is confusing as ****, if it was a standard calculation I'd have figured it out. Sadly with it being a balloon payment it seems to have complicated things a bit, I guess its because interest accumulates on the balloon payment over the full period but reduces over the course of the loan for the rest of the value. I wouldn't have thought this affected a fixed rate of interest, but apparently it must do.

Ive been given a matrix of calculations and I've posted them below. These may help. It looks like the fixed rate stays the same within a couple hundredths of a percent, but I'm still no closer to understand how the **** its derived.


term Cash price monthly payment Total amount payable Fixed rate APR deposit balloon
24 15000 194.58 16669.92 4.07 7.90% 3000 60% 9000
24 20000 259.44 22226.56 4.07 7.90% 4000 60% 12000
24 25000 482 28068 4.07 7.90% 1500 60% 15000
24 30000 569.39 33665.36 4.07 7.90% 2000 60% 18000
24 30000 591.92 33706.08 4.07 7.90% 1500 60% 18000
24 30000 253.99 33095.76 4.07 7.90% 9000 60% 18000
24 30000 434.22 33421.28 4.07 7.90% 5000 60% 18000
24 30000 659.51 33828.24 4.07 7.90% 0 60% 18000
24 35000 764.92 39458.08 4.07 7.90% 100 60% 21000
24 35000 769.42 39466.08 4.07 7.90% 0 60% 21000
30 15000 292.82 17334.6 4.06 7.90% 3000 57% 8550
30 20000 390.42 23112.6 4.06 7.90% 4000 57% 11400
30 25000 432.95 28738.5 4.06 7.90% 1500 57% 14250
30 30000 512.2 34466 4.06 7.90% 2000 57% 17100
30 30000 530.56 34516.8 4.06 7.90% 1500 57% 17100
30 30000 255.17 33755.1 4.06 7.90% 9000 57% 17100
30 30000 402.04 34161.2 4.06 7.90% 5000 57% 17100
30 30000 585.63 34668.9 4.06 7.90% 0 57% 17100
30 35000 679.57 40437.1 4.06 7.90% 100 57% 19950
30 35000 683.24 40447.2 4.06 7.90% 0 57% 19950
36 15000 170.6 17391.6 4.06 7.90% 3000 55% 8250
36 20000 227.47 23188.92 4.06 7.90% 4000 55% 11000
 
Hi guys, sorry for not replying for a few days, my wife had a baby so have been a little bit busy. Thanks so far for everyone's help. I understand the interest rate is confusing as ****, if it was a standard calculation I'd have figured it out. Sadly with it being a balloon payment it seems to have complicated things a bit, I guess its because interest accumulates on the balloon payment over the full period but reduces over the course of the loan for the rest of the value. I wouldn't have thought this affected a fixed rate of interest, but apparently it must do.

Ive been given a matrix of calculations and I've posted them below. These may help. It looks like the fixed rate stays the same within a couple hundredths of a percent, but I'm still no closer to understand how the **** its derived.


term Cash price monthly payment Total amount payable Fixed rate APR deposit balloon
24 15000 194.58 16669.92 4.07 7.90% 3000 60% 9000
24 20000 259.44 22226.56 4.07 7.90% 4000 60% 12000
24 25000 482 28068 4.07 7.90% 1500 60% 15000
24 30000 569.39 33665.36 4.07 7.90% 2000 60% 18000
24 30000 591.92 33706.08 4.07 7.90% 1500 60% 18000
24 30000 253.99 33095.76 4.07 7.90% 9000 60% 18000
24 30000 434.22 33421.28 4.07 7.90% 5000 60% 18000
24 30000 659.51 33828.24 4.07 7.90% 0 60% 18000
24 35000 764.92 39458.08 4.07 7.90% 100 60% 21000
24 35000 769.42 39466.08 4.07 7.90% 0 60% 21000
30 15000 292.82 17334.6 4.06 7.90% 3000 57% 8550
30 20000 390.42 23112.6 4.06 7.90% 4000 57% 11400
30 25000 432.95 28738.5 4.06 7.90% 1500 57% 14250
30 30000 512.2 34466 4.06 7.90% 2000 57% 17100
30 30000 530.56 34516.8 4.06 7.90% 1500 57% 17100
30 30000 255.17 33755.1 4.06 7.90% 9000 57% 17100
30 30000 402.04 34161.2 4.06 7.90% 5000 57% 17100
30 30000 585.63 34668.9 4.06 7.90% 0 57% 17100
30 35000 679.57 40437.1 4.06 7.90% 100 57% 19950
30 35000 683.24 40447.2 4.06 7.90% 0 57% 19950
36 15000 170.6 17391.6 4.06 7.90% 3000 55% 8250
36 20000 227.47 23188.92 4.06 7.90% 4000 55% 11000

It does help to have correct information.

1) The first two 30's are incorrect. The lump is not included in the Total Paid.

2) (1 + 0.0790/2)^12 - 1 = 0.08192416916978
3) #1-#10 are reproduced with effective 8.6201%
4) #13-#20 are reproduced with effective 8.4737%
5) #21-#22 are reproduced with effective 5.7267%

I think what we have, here, is a failure to obtain he right information.
 
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I think what we have, here, is a failure to obtain the right information.
Ya...much adoo about nothing!
A "balloon payment" is same as borrower deciding to pay off loan in full...
And that "4.07" is more mysterious than the holy spirit taking a hold
of you if you've recited the proper prayer with proper pronunciation...
 
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