# Compute the time it will take to pay off a credit card of 500 with a min payment of 40 dollors with a interest of 19 percent.i need to do it step by step

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Somebody out there probably has a much more efficient way to do this, but here's how i did it.

Simple interest:

I = Prt (principle * rate * time) The rate is per annum (per year). The time is in months - how many months out of the year there continues to be a balance (so, if it take 7 months, then t would be 7/12). And make sure your rate of 19% is in decimal form (.19).

To figure out interest you'd accumulate in 1 month,

I = 500(.19)(1/12) = 7.916 (7.92)

To figure out how much interest you'd accumulate in 1 year,

I = 500(.19)(12/12) = 95.00

After 1 year, accumulated interest would be 95.00. In a year, you would need to have paid 595.00.

If you paid $40 a month, by the end of one year, you would've paid $480. (40)(12) = 480. Not enough.

You'd need more months just to surpass the principle + first year's interest. But during those additional months, more interest accumulates. Let's try 15 months. So, the interest would be:

I = 500(.19)(15/12) = 118.75. So, the total after 15 months would be 618.75.

I + P is 118.75 + 500 = 618.75.

Paying $40 a month for those 15 months gives you 40(15), which is 600. Still short. Looks like it will take one more month.

I = 500(.19)(16/12) = 126.67

I + P is 126.67 + 500 = 626.67

Paying $40 a month for those 16 months gives you 40(16) = 640. 16 months paying 40/month.

The difficulty is that there is no mention of minimum payment period.

I pressume that it is a month and $40 is paid inculive of iterest each month.

The monthly interest rarte per dollar = 19%/12 = 0.19/12.

First month:

500 with monthly interest ,(500*0.19/12 = 7.9166666) = $507.1666666. minus minimum payment = $467.91666 at credit balance in the beginning of the 2nd month.

2nd month:

467.91666..+ 467*(.19/12) - 40 = 435.43253472.

Like that please continue. Here is it in Ms exel. At the end of 14th month you shal have ve acredit balance of $1.55 which could be repaid :

month_No The amount m_ intt @19%/12 amountt+intterest Min payment credit balance 1 500 7.916666667 507.9166667 40 467.9166667 2 467.916667 7.408680556 475.3253472 40 435.3253472 3 435.325347 6.892651331 442.2179986 40 402.2179986 4 402.217999 6.368451644 408.5864502 40 368.5864502 5 368.58645 5.835952128 374.4224023 40 334.4224023 6 334.422402 5.29502137 339.7174237 40 299.7174237 7 299.717424 4.745525875 304.4629496 40 264.4629496 8 264.46295 4.187330035 268.6502796 40 228.6502796 9 228.65028 3.620296094 232.2705757 40 192.2705757 10 192.270576 3.044284115 195.3148598 40 155.3148598 11 155.31486 2.459151947 157.7740118 40 117.7740118 12 117.774012 1.864755186 119.6387669 40 79.63876695 13 79.6387669 1.260947143 80.89971409 40 40.89971409 14 40.8997141 0.647578806 41.5472929 40 1.547292897 15 1.5472929 0.024498804 1.571791702 40 -38.4282083