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To calculate how long it will take to pay off a $15,000 debt at 1.6% interest by making monthly payments of $200, you can use the formula:

[ \text{Time (in months)} = -\frac{\text{Logarithm}\left(1 - \frac{\text{Monthly Interest Rate}}{\text{Loan Amount}} \cdot \text{Monthly Payment}\right)}{\text{Logarithm}\left(1 + \text{Monthly Interest Rate}\right)} ]

First, calculate the monthly interest rate, which is the annual interest rate divided by 12 (since there are 12 months in a year):

[ \text{Monthly Interest Rate} = \frac{1.6%}{12} = 0.016/12 = 0.0013333 ]

Now, plug the values into the formula:

[ \text{Time (in months)} = -\frac{\text{Logarithm}\left(1 - \frac{0.0013333}{15000} \cdot 200\right)}{\text{Logarithm}\left(1 + 0.0013333\right)} ]

Calculating this:

[ \text{Time (in months)} \approx -\frac{\text{Logarithm}(0.9866667)}{\text{Logarithm}(1.0013333)} ]

Now, calculate the logarithms:

[ \text{Time (in months)} \approx -\frac{-0.01343}{0.0006199} ]

Divide:

[ \text{Time (in months)} \approx 21.63 ]

So, it will take approximately 21.63 months to pay off a $15,000 debt at 1.6% interest by making monthly payments of $200. This is roughly equivalent to about 1 year and 9 months. Please note that this calculation assumes a fixed interest rate and doesn’t take into account factors like compounding interest or changes in the interest rate over time.

Check out this answer I got from chat GPT