Final answer:
To determine how long it will take to pay off a stereo with monthly payments of $21.45, we would need the total cost and the interest rate. Without these, we can't calculate the exact time but we can say that solely making minimum payments will significantly extend the repayment period and increase total costs due to interest.
Step-by-step explanation:
The time it takes for José to pay off the stereo depends on the total cost of the stereo, the interest rate associated with the payment plan, and the minimum monthly payment he is making. Without additional information on the total cost and interest rate, we cannot exactly determine how long it will take to pay off the stereo by making minimum payments of $21.45 per month. However, the concept here is akin to paying off a loan or credit card debt where interest accrues over time, and making only minimum payments often results in a much longer repayment period and higher total cost due to interest.
To illustrate, let's assume José has a stereo that cost $2,000 with an interest rate of 6% annually, compounded monthly. If he pays $60 a month (the 3% minimum of the initial balance), it can take well over a decade to repay due to the interest accumulating on the remaining balance. However, without the actual interest rate and balance, this is simply an example and not an exact calculation for José's situation.