Statistics & Applications

Financial Math

Easy

applied

The effective rate per annum equivalent to a nominal rate of 8% compounded semi-annually is

8.24%

8.33%

8.16%

8.06%

✅ Correct Option: 3

The nominal rate is 8% per annum, compounded semi-annually. This means the interest is applied 2 times per year.

The effective annual rate formula is:

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

where $r = 0.08$ (nominal rate) and $n = 2$ (compounding periods per year).

The rate per compounding period:

$\frac{0.08}{2} = 0.04$

Calculating the effective rate:

$(1 + 0.04)^2 - 1$

$= (1.04)^2 - 1$

$= 1.0816 - 1$

$= 0.0816$

Converting to percentage:

$0.0816 \times 100 = 8.16\%$

The effective annual rate is 8.16%.

2025: 22 May Shift 1

Which one of the following statement is incorrect about sinking fund?

2025: 29 May Shift 2

Every year the price of a motorcycle depreciates by Rs. 15000. After 12 years its price has become Rs. 50000. Then its original cost was:

2025: 21 May Shift 1

A mobile phone costing ₹50000 has a useful life of 5 years. If the annual depreciation is ₹5000, then by using a linear method, its scrap value is

2026: 19 May Shift 1

The present value of a perpetuity of ₹x at the end of every 6 months is ₹4,00,000. If money is worth 6% per annum compounded semi-annually, what is value of x ?

2025: 3 June Shift 1

A company purchased a machine for ₹ 15,00,000 and its effective life is estimated to be 10 years. A sinking fund is created for replacing the machine at the end of its effective life when its scrap value is ₹ 2,42,000. What amount company should provide, at the end of every year out of profits for the sinking fund if it accumulates an interest of 5% per annum? [Given(1.05)¹⁰=1.629]

2026: 30 May Shift 1

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. The present value of a perpetuity of ₹3120 payable at the beginning of each year, if money is worth 6% effective.	I. ₹2,00,000
B. The present value of a perpetuity of ₹5,000 payable at the end of each year, if money is worth 5% compounded annually	II. ₹1,50,000
C. The present value of a sequence of payments of ₹3,000 payable at the end of each 6 months and continuing forever, if money is worth 4% compounded semi-annually.	III. ₹1,00,000
D. The present value of a perpetuity of ₹3,000 payable at the end of each quarter, if money is worth 6% compounded quarterly	IV. ₹55,120

Choose the correct answer from the options given below:

The effective rate per annum equivalent to a nominal rate of 8% compounded semi-annually is

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