Statistics & Applications

Financial Math

Medium

applied

If the cash equivalent of a perpetuity of ₹ 300 payable at the end of each quarter is ₹ 24,000, then the rate of interest per annum is:

10%

12.5%

7.25%

✅ Correct Option: 3

For a perpetuity, present value $= \dfrac{R}{i}$ where $i$ is the rate per payment period.

So $24000 = \dfrac{300}{i}$ , giving $i = 0.0125$ per quarter.

The annual rate is $0.0125\times 4 = 0.05$ , that is 5%.

2025: 29 May Shift 2

A charity organization has a fund of Rs.2,00000 to provide annual grants to students. The grant amount each year is Rs.15,000. The fund earns an interest rate of r% per annum. If the interest earned is used entirely to provide the grants, then the annual interest rate r is:

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:

2025: 2 June Shift 1

If CAGR stands for Compound Annual Growth Rate, F.V stands for final value of an investment, P.V stands for present value of an investment and n is the number of years then

2024: 16 May Shift 1

For which one of the following purposes is CAGR (Compounded Annual Growth Rate) not used ?

2025: 13 May Shift 2

Which of the following statements about the Sinking Fund are correct?

(A) It is a fund established by a business entity by setting aside revenue over a period of time to fund a future capital expense.

(B) It is a fund established by a business entity by setting aside revenue over a period of time to fund a future repayment of a long-term debt.

(D) It is a fund that is accumulated for the purpose of paying off a financial obligation at some future designated date.

Choose the correct answer from the options given below:

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

If the cash equivalent of a perpetuity of ₹ 300 payable at the end of each quarter is ₹ 24,000, then the rate of interest per annum is:

Solution

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