Statistics & Applications

Financial Math

Medium

applied

The effective rate, which is equivalent to a nominal rate of 12% compounded semi-annually, is

13.16%

13.36%

12.36%

12.16%

✅ Correct Option: 3

The nominal rate is 12% compounded semi-annually.

The effective rate accounts for the compounding effect and represents the actual annual interest rate earned.

The formula for effective rate is:

Effective Rate $= (1 + \frac{r}{n})^n - 1$

where $r$ is the nominal rate and $n$ is the number of compounding periods per year.

For this problem:

$r = 12\% = 0.12$

$n = 2$ (semi-annually means twice per year)

Substituting into the formula:

Effective Rate $= (1 + \frac{0.12}{2})^2 - 1$

$= (1 + 0.06)^2 - 1$

$= (1.06)^2 - 1$

$= 1.1236 - 1$

$= 0.1236$

Converting to percentage:

$0.1236 \times 100 = 12.36\%$

Therefore, the effective rate is $12.36\%$ .

2026: 22 May Shift 1

Match List-I with List-II

List-I	List-II
(A) Nominal rate of return	(I) $EMI=\frac{Principal+Interest}{Period\ in\ months}$
(B) CAGR	(II) $\frac{Original\ value\ of\ the\ asset-Salvage\ value\ of\ the\ asset}{Useful\ life\ of\ the\ asset}$
(C) Flat rate method	(III) $\frac{Current\ market\ value\ of\ investment-Original\ investment\ value}{Original\ investment\ value}\times100$
(D) Annual depreciation	(IV) $\left(\frac{Investment\ at\ the\ end\ of\ investment\ period}{Investment\ at\ the\ beginning\ of\ the\ period}\right)^{\frac{1}{investment\ period}}-1$

Choose the correct answer from the options given below:

2026: 19 May Shift 1

A person has set up a sinking fund in order to have ₹ 20,000 in 10 years for his children's education. The amount to set aside each quarter into an account paying 6% per annum compounded quarterly is: [use $(1.015)^{40} = 1.8140$ ]

2025: 19 May Shift 1

Mr. Mittal invested Rs. 20,000 in a mutual fund in the year 2019. The value of the mutual fund increased to Rs. 32,000 in the year 2024. The compound annual growth rate of his investment is:

[Given $(1.6)^{1/5} = 1.098$ ]

2025: 27 May Shift 1

A person has set up a sinking fund in order to have Rs. 10,00,000 after 10 years for his child education. The amount should put bi-annually into account paying 5% per annum compounded semi-annually is: [Given $(1.025)^{20} = 1.6386$ ]

2026: 19 May Shift 2

A person has invested ₹ 20,000 in hundred-rupees bond and redeemable at the end of 10 years at 110, and paying annual dividends at 4%. The yield rate is to be 5% effective. Then which of the following statements are TRUE?

A. The annual dividend is ₹ 800.

B. The annual dividend is ₹ 1200.

C. Redemption price is ₹ 22000.

D. Redemption price is ₹ 20000.

Choose the correct answer from the options given below:

2026: 29 May Shift 1

A machine costing ₹55,000 is expected to have a useful life of 10 years and a final scrap value of ₹5,000. The annual depreciation charge using the straight line method is :

The effective rate, which is equivalent to a nominal rate of 12% compounded semi-annually, is

Solution

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