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From: MisterE on 6 Mar 2007 01:51
I am trying to find the out the optimal way to distribute extra repayments
over 2 loans that cannot be 'refinanced' together:

$100,000 at 6% PA
and $20,000 @ 10% PA.

The minimum repayments are say $1,000 per month on the $100,000 and $500 per
month on the $20,000 loan. If I have a total of $2500 per month to spend on
both loans until I have paid out both, where do I put the extra $1,000? On
the 20,000 or 100,000? Or is it more optimal to split the $1000 into two
payments based on some sort or ratio of the loaned amounts and interest
rates.

AFAIK it doesn't matter which way you repay it, the total interest and
therefore the total time before both loans are full repaid will not change.
Is this correct?


From: Michael on 6 Mar 2007 02:59
On Mar 5, 10:51 pm, "MisterE" <v...(a)sometwher.world> wrote:
> I am trying to find the out the optimal way to distribute extra repayments
> over 2 loans that cannot be 'refinanced' together:
>
> $100,000 at 6% PA
> and $20,000 @ 10% PA.
>
> The minimum repayments are say $1,000 per month on the $100,000 and $500 per
> month on the $20,000 loan. If I have a total of $2500 per month to spend on
> both loans until I have paid out both, where do I put the extra $1,000? On
> the 20,000 or 100,000? Or is it more optimal to split the $1000 into two
> payments based on some sort or ratio of the loaned amounts and interest
> rates.

Your best bet is to pay off the one with the higher interest rate
first. Make the minimum payment on the other, and use all remaining
money for the high interest one until that's paid off.


> AFAIK it doesn't matter which way you repay it, the total interest and
> therefore the total time before both loans are full repaid will not change.
> Is this correct?

No.

To make matters really simple, suppose you have
$10,000 at 6% PA
and $10,000 @ 10% PA,
interest acrues annually,
minimum payments of 0,
and you have $10,000 a year to pay it off.

Case 1:
At the beginning of year 1, pay off 10%.
At the beginning of year 2, you'll owe 10,600 (= 10K + 6% interest).
Pay another 10K.
You still owe $636 (= $600 + 6% interest). Pay it off.
Total paid: $20,636.

Case 2:
At the beginning of year 1, pay off 6%.
At the beginning of year 2, you'll owe 11,000 (= 10K + 10% interest).
Pay another 10K.
You still owe $1,100 (= 1,000 + 10% interest). Pay it off.
Total paid: $21,100.

Your example is obviously more convoluted, but the same principle
applies.

Another way to look at it: at some point in time, suppose you have X
left in the 6% account and Y left in the 10% account. You pay off a
to the 6% account and b to the 10% account, where a+b=2500.

The interest you owe in the next month is:
(X - a) * 6%/12 + (Y - b) * 10%/12
= (X - a) * 6%/12 + (Y - b) * (6%/12 + 4%/12)
= (X + Y - (a + b)) * 6%/12 - (Y - b) * 4%/12
= (X + Y - (2500)) * 6%/12 - (Y - b) * 4%/12

To minimize the interest, you want to maximize b.

Michael

From: Michael Press on 8 Mar 2007 21:53
In article
<45ed0f5c$0$21144$afc38c87(a)news.optusnet.com.au>,
"MisterE" <voids(a)sometwher.world> wrote:

> I am trying to find the out the optimal way to distribute extra repayments
> over 2 loans that cannot be 'refinanced' together:
>
> $100,000 at 6% PA
> and $20,000 @ 10% PA.
>
> The minimum repayments are say $1,000 per month on the $100,000 and $500 per
> month on the $20,000 loan. If I have a total of $2500 per month to spend on
> both loans until I have paid out both, where do I put the extra $1,000? On
> the 20,000 or 100,000? Or is it more optimal to split the $1000 into two
> payments based on some sort or ratio of the loaned amounts and interest
> rates.
>
> AFAIK it doesn't matter which way you repay it, the total interest and
> therefore the total time before both loans are full repaid will not change.
> Is this correct?

Would you _invest_ your money at 6% or 10%?

--
Michael Press
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