Final answer:
Calculating how long it will take to pay off a $50,000 loan with a 6% annual interest rate compounded monthly and monthly payments of $600 requires an amortization calculation or a financial calculator, as the formula is complex.
Step-by-step explanation:
To determine how long it will take to pay off a loan of $50,000 at an annual rate of 6% compounded monthly with monthly payments of $600, we can use the amortization formula or a financial calculator. Calculating loan payments and payoff times involves understanding the relationship between principal, interest rate, and time. The formula for the monthly payment on an amortizing loan is:
M = P [i(1+i)^n] / [(1+i)^n – 1]
Where:
- M is the monthly payment.
- P is the principal amount.
- i is the monthly interest rate (annual rate divided by 12).
- n is the number of payments (months).
Since an exact formula for solving for 'n' is complex due to its position in the formula, a financial calculator or spreadsheet is often used to find the precise duration.