Final answer:
The interest rate compounded semi-annually equivalent to 6% compounded monthly can be calculated using a conversion formula. In the context of loans, this conversion is relevant for understanding equivalent interest rates for different compounding periods, and making additional payments can save on the total interest and repayment duration.
Step-by-step explanation:
To calculate the interest rate compounded semi-annually that is equivalent to a nominal annual interest rate compounded monthly (J12=6%), we need to use the formula for converting nominal interest rates compounded differently. The formula to find the equivalent semi-annual interest rate (J2) is given by:
(1 + J2/2)2 = (1 + J12/12)12
Substituting J12 = 0.06 into the equation gives us:
(1 + J2/2)2 = (1 + 0.06/12)12
After calculating the right side, we can then solve for J2 to get the semi-annual rate.
Example calculations like determining the monthly payment for a house loan or the future value of an investment are based on similar principles of compound interest.