Question

Explain why the following statement is false.

If a long-term note payable has a stated interest rate, that rate should be considered to be the effective rate.

Answer 1

Stated interest rate of a bond, signifies the actual monetary price borrower pay lenders to use their money. This interest does not take effect of compound interest into account. For Example, if the stated interest rate of Bond X is 8%, borrowers can expect to pay $8 of interest for every $100 loaned to them.

Where as, Effective interest rate takes into account the effect of compounding and hence used to calculate the true interest of the bond.

Mathematically speaking, the difference between the stated rate and effective rate increases with the number of compounding periods within a specified time period. Therefore in case of a long term payable bond, the number of compounding period causes the difference between stated rate and effective rates.

For example, if a bond pays 10% annually and compounds semiannually, an investor who places $1,000 in this bond will receive $50 of interest payments after the first 6 months ($1,000 x .05), and $52.50 of interest after the next six months ($1,050 x .05). In total, this investor receives $60.90 for the year. In this scenario, while the nominal rate is 10%, the effective rate is 10.25%

Hence, because of the above stated reasons and example, the statement is false.