Statistics & Applications

Financial Math

Medium

applied

The effective rate equivalent to a nominal rate of 12% compounded quarterly is: (Given $(1.03)^4=1.1256$ )

14.25%

12.56%

10.36%

12%

✅ Correct Option: 2

The nominal rate is 12% per year, compounded quarterly.

When compounding quarterly, the interest is applied 4 times per year.

Quarterly rate $= \dfrac{12\%}{4} = 3\% = 0.03$

The effective annual rate formula when compounding occurs multiple times per year:

Effective Rate $= (1 + r)^n - 1$

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

Substituting the values:

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

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

Given that $(1.03)^4 = 1.1256$ :

Effective Rate $= 1.1256 - 1$

Effective Rate $= 0.1256$

Converting to percentage:

Effective Rate $= 0.1256 \times 100 = 12.56\%$

Therefore, the effective rate equivalent to a nominal rate of 12% compounded quarterly is 12.56%.

2025: 22 May Shift 2

Rahul invested ₹ 20000 in a mutual fund in year 2018. If the value of mutual fund increased to ₹ 32000 in year 2023. Then the compound annual growth rate of his investment is: $[given \, that(1.6)^{1/5} = 1.098]$

2025: 14 May Shift 1

A person wishes to purchase a house for ₹ 39,65,000 with a down payment of ₹ 5,00,000 and balance in equal monthly installments (EMI) for 25 years. If bank charges 6% per annum (compounded monthly), then EMI on reducing balance payment method is:

[Given $(1.005)^{300} = 4.465$ ]

2026: 19 May Shift 2

Amit invested ₹ 25,000 in a no-fee fund. After one year, the value of the fund rose to ₹ 30,000 then the nominal rate of return on the investment is

2024: 16 May Shift 1

Match List-I with List-II:

List-I Property Type	List-II EMI amount (in ₹)
(A) P	(I) 25,600
(B) Q	(II) 38,400
(C) R	(III) 32,000
(D) S	(IV) 35,200

2025: 21 May Shift 1

Which of the following is correct about the compound annual growth rate(CAGR)?

2025: 26 May Shift 2

Vatsala buys a car for Rs.7,00,000 and pays upfront Rs.2,50,000 through her credit card. The balance is to be paid in 5 years by equal monthly installments at an interest of 7% per annum as reducing balance. The EMI to be paid by Vatsala will be :- [given (1.0058)⁻⁶⁰=0.7068]

The effective rate equivalent to a nominal rate of 12% compounded quarterly is: (Given (1.03)4=1.1256(1.03)^4=1.1256(1.03)4=1.1256)

Solution

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The effective rate equivalent to a nominal rate of 12% compounded quarterly is: (Given $(1.03)^4=1.1256$ )