thomas has a loan with a nominal interest rate of 6.4624% and an effective interest rate of 6.4715%. which…
thomas has a loan with a nominal interest rate of 6.4624% and an effective interest rate of 6.4715%. which of the following must be true? i. the loan has a duration greater than one year. ii. the interest on thomass loan is compounded more than once yearly. iii. the economy was strong when thomas took out the loan. a. i and ii b. ii only c. i and iii d. iii only
Answer
Explanation:
Step1: Recall interest - rate formula
The formula for the effective - interest rate $r_{eff}$ is $r_{eff}=(1 + \frac{r_{nom}}{n})^{n}-1$, where $r_{nom}$ is the nominal interest rate and $n$ is the number of compounding periods per year. When $n = 1$ (compounded annually), $r_{eff}=r_{nom}$.
Step2: Analyze given rates
Given $r_{nom}=6.4624%$ and $r_{eff}=6.4715%$. Since $r_{eff}>r_{nom}$, from the formula $r_{eff}=(1 + \frac{r_{nom}}{n})^{n}-1$, we know that $n>1$, which means the interest is compounded more than once a year.
Step3: Evaluate each statement
- Statement I: The duration of the loan is not related to the difference between nominal and effective interest rates. The formula for effective interest rate does not depend on the loan duration.
- Statement II: As shown above, since $r_{eff}>r_{nom}$, $n > 1$, so the interest is compounded more than once a year.
- Statement III: The strength of the economy when the loan was taken out has no bearing on the relationship between the nominal and effective interest rates for a given loan.
Answer:
B. II only