To compute the periodic interest rate $i$, as a decimal, we use the formula:

$i = \frac{r}{n}$

Where:

• $r$ is the nominal annual interest rate (as a decimal).
• $n$ is the number of compounding periods per year.

(a) 8.88% per year, compounded quarterly:

• $r = 8.88\% = 0.0888$
• $n = 4$ (quarterly compounding)

$i = \frac{0.0888}{4} = 0.0222$

Answer: $i = 0.0222$

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(b) 9.55% per year, compounded semiannually:

• $r = 9.55\% = 0.0955$
• $n = 2$ (semiannual compounding)

$i = \frac{0.0955}{2} = 0.0478$

Answer: $i = 0.0478$

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(c) 7.07% per year, compounded daily:

• $r = 7.07\% = 0.0707$
• $n = 365$ (daily compounding)

$i = \frac{0.0707}{365} \approx 0.0002$

Answer: $i = 0.0002$

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Final Results:

(a) $i = 0.0222$
(b) $i = 0.0478$
(c) $i = 0.0002$

Would you like further explanation or help with similar computations?

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Related Questions:

1. What is the significance of periodic interest rates in loan calculations?
2. How does the number of compounding periods affect the effective annual rate?
3. Can you compute the effective annual rate for these scenarios?
4. What is the relationship between nominal and periodic rates in simple interest?
5. How does daily compounding compare to monthly compounding for the same nominal rate?

Tip:

Always ensure nominal rates are converted into decimals before performing calculations to avoid errors.