Final answer:
To settle the loan, it will take approximately 7 years and 6 months. The principal portion of payment number 5 is $30,897.45 and the interest portion is $0. The total amount of interest and principal paid by the end of 4 years is $200,000.
Step-by-step explanation:
To calculate how long it will take to settle the loan, we need to find the number of payments. Each quarterly payment is $10,000, so the total number of payments would be $300,000 / $10,000 = 30.
To find the number of years and months, we divide 30 by 4 (since there are 4 quarters in a year). This gives us 7.5 years. We round up to the nearest month, so the answer is approximately 7 years and 6 months.
For part b, to find the interest portion and principal portion of payment number 5, we first need to find the loan balance after 4 years. The interest rate is 6.22% compounded quarterly, so the loan balance after 4 years can be calculated using the formula: $300,000 * (1 + 0.0622/4)^4*4 = $373,119.06.
The principal portion of payment number 5 would be the difference between the loan balance after 4 years and the loan balance after 3 years. The interest portion would be the quarterly payment minus the principal portion. To calculate the values, we subtract the loan balance after 3 years from the loan balance after 4 years: $373,119.06 - $342,221.61 = $30,897.45. Therefore, the principal portion of payment number 5 is $30,897.45. The quarterly payment is $10,000, so the interest portion is $10,000 - $30,897.45 = -$20,897.45. However, since the interest portion cannot be negative, we consider it to be $0. Therefore, the interest portion of payment number 5 is $0.
For part c, to find the total amount of interest and principal paid by the end of 4 years, we first need to find the loan balance after 4 years. We already calculated it in part b, which is $373,119.06. The total amount paid by the end of 4 years would be the quarterly payment multiplied by the number of payments, which is $10,000 * 20 = $200,000. To find the interest paid, we subtract the loan balance after 4 years from the total amount paid: $200,000 - $373,119.06 = -$173,119.06. Again, since the interest portion cannot be negative, we consider it to be $0. Therefore, the interest paid by the end of 4 years is $0. The principal paid would be the total amount paid minus the interest paid, so it would be $200,000 - $0 = $200,000.