Final answer:
To calculate the total cost of the loan, find the monthly payment and multiply it by the number of months in the loan term. The total cost of Colleen's loan if paid off 8 years early would be approximately $193,958.16.
Step-by-step explanation:
To calculate the total cost of the loan, you need to find the monthly payment and multiply it by the number of months in the loan term. The formula to calculate the monthly payment is:
Monthly Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where P is the principal amount, r is the monthly interest rate, and n is the total number of monthly payments. In this case, P = $145,000, r = 4.5% / 12 = 0.375%, and n = 30 * 12 = 360.
Once you have the monthly payment, multiply it by the number of months remaining in the loan term to get the total cost of the loan if paid off early. In this case, if Colleen pays off the loan 8 years early, there would be 30 * 12 - 8 * 12 = 264 monthly payments remaining. Therefore, the total cost of the loan would be:
Total Cost = Monthly Payment * Number of Months Remaining
Now, simply substitute the values into the formula to calculate the total cost of the loan.
After performing the calculation with the given values, the approximate total cost of Colleen's loan if she paid it off 8 years early would be $193,958.16.
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