How long will it take to pay off a loan of

​$46 comma 00046,000

at an annual rate of

99​%

compounded monthly if you make monthly payments of

​$400400

​(round up)?

To determine how long it will take to pay off the loan, we can use the formula for the time $ n $ (in months) to pay off a loan when making fixed monthly payments, based on the loan balance $ P $, the monthly payment amount $ M $, and the monthly interest rate $ r $.

The formula for the number of months to pay off a loan is:

\[
n = \frac{\log\left(\frac{M}{M - P \times r}\right)}{\log(1 + r)}
\]

Where:
- $ P $ is the principal loan amount
- $ M $ is the monthly payment
- $ r $ is the monthly interest rate (annual rate divided by 12)
- $ n $ is the number of months

### Given:
- $ P = 46,000 $ (loan principal)
- Annual interest rate $ = 99\% $ → Monthly interest rate $ r = \frac{99\%}{12} = \frac{0.99}{12} $
- $ M = 400 $ (monthly payment)

Let's calculate $ n $.It seems there was an issue with the calculation, which typically happens when the monthly payment is too low to cover the monthly interest on the loan. This occurs when $ M - P \times r $ becomes negative or zero, meaning the loan cannot be paid off with the given monthly payments of $400.

In this case, the loan balance and interest rate are too high for a $400 monthly payment. You would need to increase the monthly payment to pay off the loan eventually.

Would you like to calculate the minimum required monthly payment or discuss alternative approaches?

How long will it take to pay off a loan of $46,000 at an annual rate of 99% compounded monthly if you make monthly payments of $400 (round up)?

Learn how to calculate the time required to pay off a $46,000 loan at an annual interest rate of 99%, compounded monthly, with $400 monthly payments. This problem involves key financial concepts, including loan amortization and logarithmic functions. Suitable for college-level finance or mathematics students.

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