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A simple varient, if you know your payments, rate, etc, and want to know what happens to your debt as months pass:
D(n) = P/R - (P/R - D(0))*(1+R)^n
Fill in everything except for n.
So, for example, you are paying 300$ a month towards a 10,000$ debt with 1% monthly interest.
So,
D(0) = 10000
P = 300
R = 0.01
D(n) = 300/0.01 - (300/0.01 - 10000) * (1.01)^n
D(n) = 30000 - 20000 * (1.01)^n
D(6 months) = 8769.60
D(12 months) = 7463.50
D(24 months) = 4605.31
D(36 months) = 1384.62
D(40 months) = 222.73
D(41 months) = -75.05
If you know how long, but don't know how much you are paying, fill in everything except for P into:
D(n) = D(0)*(1+R)^n - P * ((1+R)^n - 1)/R
So, 10,000$ debt, 0.01% interest, over 6 months.
D(6 months) = 10000 * (1.01)^6 - P * (1.01^6-1)/0.01
= 10615.20 - P * 6.15
If P = 100, we end up with 10,000$. As expected: we only payed interst.
P = 200 means D(6) = 9385
P = 300 means D(6) = 8770
P = 400 means D(6) = 8154
P = 1000 means D(6) = 4460
Looking at the equation:
D(n) = D(0)*(1+R)^n - P * ((1+R)^n - 1)/R
This part: (1+R)^n - 1)/R is the "multiplier factor". That is how many dollars of debt you eat away when you put 1$/month towards your debt. In the above example, it was 6.15.
If you have 1% monthly interest, and you pay regularly for a year, every dollar reduces your debt at the end by:
12.68$
Do that for two years, every dollar/month reduces your debt by almost 27$. 3 free dollars! ;-)
Ok, I'm pretty confident the formulas work!
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Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.
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