Question

check your understanding

1. copy and complete the table.

	compound interest rate per annum (%)	compounding frequency	term	interest rate per compounding period (%)	number of compounding periods
	4.1	monthly	6 years
	13.2	quarterly	7 years
	3.5	daily	9 months

Explanation:

Step1: Define formulas

Rate per period: $r = \frac{\text{Annual Rate}}{\text{Compounding Frequency}}$
Number of periods: $n = \text{Term} \times \text{Compounding Frequency}$
(Assume 365 days for daily compounding)

Step2: Row 1 (10.2%, semi-annual, 4y)

Calculate rate per period:
$r = \frac{10.2}{2} = 5.1$
Calculate number of periods:
$n = 4 \times 2 = 8$

Step3: Row 2 (4.1%, monthly, 6y)

Calculate rate per period:
$r = \frac{4.1}{12} \approx 0.34$
Calculate number of periods:
$n = 6 \times 12 = 72$

Step4: Row3 (13.2%, quarterly,7y)

Calculate rate per period:
$r = \frac{13.2}{4} = 3.3$
Calculate number of periods:
$n = 7 \times 4 = 28$

Step5: Row4 (3.5%, daily,9mo)

Convert term to years: $9 \text{ mo} = \frac{9}{12} = 0.75 \text{ y}$
Calculate rate per period:
$r = \frac{3.5}{365} \approx 0.0096$
Calculate number of periods:
$n = 0.75 \times 365 = 273.75 \approx 274$

Answer:

Compound Interest Rate per Annum (%)	Compounding Frequency	Term	Interest Rate per Compounding Period, r (%)	Number of Compounding Periods, n
4.1	monthly	6 years	$\approx0.34$	72
13.2	quarterly	7 years	3.3	28
3.5	daily	9 months	$\approx0.0096$	274