Final answer:
Calculating the time it will take for Tammy to pay off a $30,000 debt with a 23% APR and $600 monthly payments requires using a debt repayment formula and typically a financial calculator or online tool, as this calculation involves solving for an exponent.
Step-by-step explanation:
To calculate how long it will take Tammy to pay off her $30,000 credit card debt with a 23 percent APR (compounded monthly) and monthly payments of $600, we need to use the debt repayment formula. The formula for the monthly payment on an installment loan is given by:
A = P * (r(1+r)^n) / ((1+r)^n - 1)
Where A is the monthly payment amount, P is the principal amount ($30,000), r is the monthly interest rate (APR divided by 12 months), and n is the total number of payments (months).
However, since we have the monthly payment but want to find the number of months 'n', we will rearrange the formula. Calculating 'n' requires an iterative approach or a financial calculator because it involves solving for the variable in the exponent.
Given these complexities, it's common to use a financial calculator, an online debt repayment calculator, or a spreadsheet tool with built-in financial functions to determine the exact number of months required. The monthly interest rate is 23% APR divided by 12 months, which equals approximately 1.917% monthly. The formula will then be rearranged to solve for 'n' given the monthly interest rate, the principal amount, and the monthly payment amount.
As the exact calculation without financial tools involves complex logarithmic functions, it is recommended to use such tools for an accurate number of months. By plugging in the values into an online calculator or a financial calculator, we can find out the number of months it would take Tammy to pay off her $30,000 debt at the rate of $600 a month.