Final answer:
The interest paid on a $26,000 loan at 6% interest over 4 years varies depending on the compounding frequency - annually, semiannually, quarterly, monthly, or continuously - requiring different calculations for each scenario.
Step-by-step explanation:
To calculate the interest paid on a $26,000 loan over 4 years at an interest rate of 6%, we use the compound interest formula: A = P(1 + r/n)nt, where A is the amount on the loan, P is the principal amount ($26,000), r is the annual interest rate (0.06), n is the number of times interest is compounded per year, and t is the time the money is invested or borrowed for (4 years). We solve for A in each case and then subtract the principal to find the interest paid.
- Annually: n=1, Interest paid = A - P
- Semiannually: n=2, Interest paid = A - P
- Quarterly: n=4, Interest paid = A - P
- Monthly: n=12, Interest paid = A - P
- Continuously: A = Pert, Interest paid = A - P
(For the continuous compound interest, 'e' represents the Euler's number, approximately equal to 2.71828.) To get the direct answers, one must perform the calculations for each compounding frequency.