Statistics & Applications

Financial Math

Medium

applied

The effective rate of return equivalent to a nominal rate of 12% per annum compounded quarterly is: [Given that: $(1.03)^4 ≈ 1.1255$ ]

13.55%

12.55%

11.55%

14.25%

✅ Correct Option: 2

The effective annual rate needs to be found when the nominal rate is 12% per annum compounded quarterly.

Compounding happens 4 times a year, so interest is earned on interest, resulting in an actual return greater than 12%.

Nominal rate = 12% per annum

Compounding = Quarterly (4 times a year)

Rate per quarter = 12% ÷ 4 = 3% per quarter

The annual rate is split into 4 equal parts, one for each quarter.

The effective rate formula is:

Effective Rate = $(1 + \text{Rate per period})^{\text{Number of periods}} - 1$

Rate per period = 3% = 0.03

Number of periods = 4

Effective Rate = $(1 + 0.03)^4 - 1$

Effective Rate = $(1.03)^4 - 1$

Given that $(1.03)^4 ≈ 1.1255$ :

Effective Rate = $1.1255 - 1$

Effective Rate = $0.1255$

Converting to percentage:

$0.1255 = 0.1255 \times 100\% = 12.55\%$

Therefore, the effective rate of return is 12.55%.

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The effective rate of return equivalent to a nominal rate of 12% per annum compounded quarterly is: [Given that: (1.03)4≈1.1255(1.03)^4 ≈ 1.1255(1.03)4≈1.1255]

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The effective rate of return equivalent to a nominal rate of 12% per annum compounded quarterly is: [Given that: $(1.03)^4 ≈ 1.1255$ ]