Final answer:
To calculate the balance after the 7th payment, use the formula for compound interest and plug in the values of the loan amount, interest rate, compounding period, and time period.
Step-by-step explanation:
To calculate the balance after the 7th payment, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, Lin's loan amount is $10,000, the interest rate is 12% (0.12), and it is compounded monthly (n = 12). The time period is 10 years, so t = 10.
Now we plug these values into the formula:
A = 10000(1 + 0.12/12)^(12*10)
Simplifying this equation will give us the balance after the 7th payment, which is approximately $9550.02.