Question

Suppose $26,000 is borrowed for 4 years at 6% interest. Find the interest paid over this period if the interest is compounded as follows.

(a) Annually
(b) Semiannually
(c) Quarterly
(d) Monthly
(e) Continuously

Answer 1

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.

1. Annually: n=1, Interest paid = A - P
2. Semiannually: n=2, Interest paid = A - P
3. Quarterly: n=4, Interest paid = A - P
4. Monthly: n=12, Interest paid = A - P
5. 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.