# Looking for final interest payment on a loan just paid off

• May 15th 2012, 07:42 PM
Tlmuntain
Looking for final interest payment on a loan just paid off
Hi there,
It has been over 7 years since I have had to use any of my mathematics of finance knowledge and wow does it disappear when you do not use it.
i have pulled out my old books to determine additional payments to a P.V. (geese, at least I think that's the formula I want) but I cannot remember how to execute the problem. Can someone please help.
Here are the values...
interest rate is 8% c.s.a.
loan with interest as of Sept. 1 2011
= \$31 938.59

Regular payments of \$1000 per month starting Sept 1st.

On top of the \$1000 payment, an additional payment of \$5000 was made on Dec 1 st 2011
Not knowing the interest amount, I have paid of the rest of the principle on May 1st totaling \$17 938.59
i would like to figure out the balance of the loan owing, which should only be the interest from Sept 1.

The formula I think I should be using is:

31938.59=1000[1-(1+I)-n]
______
I

Then I would need to find the balance on the 8th payment???

Help please! I am a business owner, not in school anymore :). Although maybe I should be! Lol
• May 16th 2012, 04:32 AM
Tlmuntain
Re: Looking for final interest payment on a loan just paid off
I have I think figured out that...
Pv=-31938.59
I=.04
N=8
Because there is no real ending term of time with the loan, should I enter in eight months since that's the time it took to pay it off?
• May 17th 2012, 07:33 AM
Wilmer
Re: Looking for final interest payment on a loan just paid off
Quote:

Originally Posted by Tlmuntain
Here are the values...
interest rate is 8% c.s.a.
loan with interest as of Sept. 1 2011
= \$31 938.59

Regular payments of \$1000 per month starting Sept 1st.

On top of the \$1000 payment, an additional payment of \$5000 was made on Dec 1 st 2011
Not knowing the interest amount, I have paid of the rest of the principle on May 1st totaling \$17 938.59
i would like to figure out the balance of the loan owing, which should only be the interest from Sept 1.

My fellow Canadian, you are more confusing than my mother-in-law!

Your loan amount (INCLUDING INTEREST calculated as if \$1000 will be paid monthly and nothing else!)
at Sep 1st/11 is really 30,938.50: due to payment made Sep 1st ...... RIGHT?
So if you stuck to \$1,000 monthly, your final payment would be 938.59...RIGHT?

And this: "interest rate is 8% c.s.a."
means compounded semi-annually...RIGHT?
Boy, wonder why we still do that...started in the 1800's I think, when farmers
paid back farm loans twice yearly, to match income from early crops and later crops!

The interest to use is the MONTHLY equivalent to the semi-annual rate, thusly:
(1 + i)^12 = 1.04^2 ; works out to i = .006558... per month;
as example, \$20,000 for 1 month means interest of 20000 * .006558 = \$131.16

We need the amount of loan WITHOUT interest...or the loan's cash proceeds:
that's the Present Value of 31 monthly payments of \$1,000 (\$30,938, so 31 close enough):
that works out to \$27,970 (give or take a Loonie...worth 1.01583...USA!)

After 7 payments of \$1,000 (to Apr 1st) plus your extra payment of \$5,000, the \$27,970
reduces to \$17.007 as at Apr 1st: so when you walked in to pay off on May 1st,
17,007 + 113 (interest for April) = 17,120 was owing.

Since you paid 17,938, then owing to you should be 17938 - 17120 = \$818.

Ok, above is a close as I can make it with the info you've given.
Let me know if you need more.

Here's what a "loan account statement" would look like:
Code:

```DATE  PAYMENT INTEREST BALANCE Sep 1                    27970 Oct 1  -1000    183      27153 Nov 1  -1000    178      26331 Dec 1  -6000    173      20504 Jan 1  -1000    134      19638 Feb 1  -1000    129      18767 Mar 1  -1000    123      17890 Apr 1  -1000    117      17007 May 1          113      17120```
• May 17th 2012, 10:26 AM
Tlmuntain
Re: Looking for final interest payment on a loan just paid off
Lol, but not as confusing as my mother-in-law !

Here is my chart from G/L
Yes case means semi-annually lol
The prospect of the loan was to pay 1000 until we could pay them in full.
My last fiscal year end was August 31, 2011 where the balance owing including interest was
31938
So here my table
Date. Payment. Balance no interest added
August 31 31938
Sept 1. 1000. 30938
Oct 1. 1000. 29938
Nov 1. 1000. 28938
Dec 1. 6000. 22938
Jan 1. 1000. 21938
Feb 1. 1000. 20938
Mar 1. 1000. 19938
Apr 1. 1000. 18938
May 1. 18938. 0

Now I just need the interest amount owing on the loan from sept 1 till the payout on may 1 st.
I hope that is clearer lol :). AND to make it more confusing, I am not sure if hey will charge me 5 or 8 percent interest. Depends on how close they read the contract, I SHOULD be paying eight percent but they may only charge me five. Both C.S.A.
Thank you for helping me, I think I sounded confusing because I tried on my own for two hours before reaching out for help lol
• May 17th 2012, 10:27 AM
Tlmuntain
Re: Looking for final interest payment on a loan just paid off
Sorry, it didn't space out as nicely as I had typed it in!
• May 17th 2012, 11:03 AM
Wilmer
Re: Looking for final interest payment on a loan just paid off
Quote:

Originally Posted by Tlmuntain
My last fiscal year end was August 31, 2011
where the balance owing including interest was 31938

Geezzzzz TL: does that mean
1: including interest up to that point
or
2: including all future interest

I assumed you meant #2.
• May 17th 2012, 11:16 AM
Tlmuntain
Re: Looking for final interest payment on a loan just paid off
Including interest to that point.
They have given me the interest accrued at my year ends which I have entered into my books. Therefore the 31938 was interested up to that point.
• May 17th 2012, 11:22 AM
Tlmuntain
Re: Looking for final interest payment on a loan just paid off
if I take .006558 and multiply that to each of my balances in my table, would that then give me the interest...ex
30938 x .006558 = 202.89
So then my balance due the end of sept would be 31140.
Then 1000 was paid oct 1st bringing it to 30140
Calculate interest again = 197.46
So balance due end of oct would be 29912
Etc etc .?? Is it hat simple? Was I trying to complicate it too much?
• May 17th 2012, 12:22 PM
Wilmer
Re: Looking for final interest payment on a loan just paid off
Not quite; this way:
Code:

```DATE  PAYMENT INTEREST BALANCE Sep 1                    30938 Oct 1  -1000    203      30141 Nov 1  -1000    198      29339 Dec 1  -6000    192      23531 Jan 1  -1000    154      22685*** Feb 1  -1000    149      21834 Mar 1  -1000    143      20977 Apr 1  -1000    138      20115 May 1          132      20247```
Total interest = 1309

***example: 22685 * .006558 = 148.77 : becomes end of Jan interest...