Answer: Barry would save approximately $15,208.08 by paying off the loan 8 years early.
Explanation:
To calculate how much Barry would save by paying off the loan 8 years early, we first need to calculate the total amount of interest he would pay over the remaining 8 years.
We can use the formula for calculating the remaining balance on a loan:
Balance = (P * ((1 + r/n)^(nt)) - (A * (((1 + r/n)^(nt)) - 1)/(r/n)))
where:
P = principal amount (initial loan amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = time (in years)
A = monthly payment
Substituting the given values in the formula, we can calculate the remaining balance:
Balance = ($55,000 * ((1 + 0.068/12)^(1220)) - ($419.84 * (((1 + 0.068/12)^(1220)) - 1)/(0.068/12)))
Balance = $31,019.97
Now, we need to calculate the total interest paid over the remaining 8 years. We can do this by subtracting the remaining balance from the total amount of interest that would be paid over the entire 20-year loan term:
Total interest paid over 20 years = (A * 12 * 20) - P
Total interest paid over 20 years = ($419.84 * 12 * 20) - $55,000 = $50,969.63
Total interest paid over the remaining 8 years = (A * 12 * 8) - Balance
Total interest paid over the remaining 8 years = ($419.84 * 12 * 8) - $31,019.97 = $35,761.58
Therefore, Barry would save approximately $15,208.08 by paying off the loan 8 years early.