Final answer:
After borrowing $18,000 at a 4.25% interest rate compounded quarterly for 8 years, you will have to pay approximately $26,409.16 by the end of the term.
Step-by-step explanation:
To calculate the amount you will have to pay at the end of the loan term with compound interest, you can use the formula for the future value of a compound interest investment: A = P(1 + r/n)^(nt). Here, A is the amount of money accumulated after n years, including interest, P is the principal amount ($18,000), r is the annual interest rate (4.25%), n is the number of times that interest is compounded per year (quarterly, so 4 times), and t is the time the money is invested for in years (8 years). Using these values, the calculation is as follows:
- Convert the interest rate from a percentage to a decimal by dividing by 100: 4.25% / 100 = 0.0425.
- Divide the annual rate by the number of compounding periods per year: 0.0425 / 4 = 0.010625.
- Add 1 to the above result: 1 + 0.010625 = 1.010625.
- Raise this result to the power of the total number of compounding periods: (1.010625)^(4*8) = (1.010625)^32.
- Finally, multiply the principal amount by the result from step 4 to find the future value: $18,000 * (1.010625)^32 = $26,409.16 (rounded to two decimal places).
Therefore, at the end of the eight years, you would have to pay approximately $26,409.16.