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 Post subject: Optimizing 3 loan repaymentsPosted: Thu, 15 Mar 2012 03:06:24 UTC
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Joined: Wed, 14 Mar 2012 11:33:58 UTC
Posts: 1
Hi,

I have the following problem about optimizing my loan repayments.

Got 3loans
A 6000 @ 10.5%p/a min. per month 140 Increase per month 52.50 [6000*(10.5%/12)]
B 10000 @ 6.5%p/a min. per month 100 Increase per month 54.17
C 5000 @ 3.5/a min. per month 100 Increase per month 14.58
All compounded monthly.

I have available 700 per month to repay each of these loans
After paying the minimum I have left 360.

How do I distribute the remainder so that I minimize the total interest paid at the end of each loan?
Is minimizing the total interest paid at the end of each loan the same as minimizing the time until I’ve till repaid all loans?

I believe I should be able to repay all of these loans in 3.5 to 4years, assuming I keep paying 700 per month.
I’ve though of two strategies

A) The remainder goes to the loans which increase due interest is highest, i.e. all to B (for the first period)
B) The remainder gets spit up by ratio, i.e. A gets mimimum + 360 * ( 52.5 / [52.50+54.17+14.58] )

Can anyone proof / disproof to me mathematically that my repayments are optimized?

Things to note;

After paying of one loan, I have more money available for repaying the others.
Increase per month depends on current value, hence increase per month will decline each month.
Distribution of the remainder will change per period.

I’m stuck with this problem for a while now, using excel to go over each strategy period by period yields pretty much the same result, payback in 42monhts, total interest paid about 1500.

Jack

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 Post subject: Re: Optimizing 3 loan repaymentsPosted: Thu, 15 Mar 2012 07:20:37 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3692
Location: Ottawa Ontario
You'll be all paid up in 33 months:
Code:
MN         10.5%                  6.5%                  3.5%
00               6000                  10000                 5000
01  -500                    -100                      -100
...
13  -367         PAID       -233        9251          -100   3870
14                          -600                      -100
...
30                          - 87        PAID          -613   1813
31                                                    -700
32                                                    -700
33                                                    -422   PAID

10.5% loan paid in 13 months; overpayment going against 6.5% loan
6.5% loan paid in 30 months; overpayment going against 3.5% loan
3.5% loan paid in 33 months; overpayment of \$278 in your pocket!

Let me know if not clear...

_________________
I'm not prejudiced...I hate everybody equally!

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