Statistics & Applications

Financial Math

Medium

applied

Rs. 2,50,000 cash is equivalent to a perpetuity of Rs.7500 payable at the end of each quarter. Then the rate of interest is

4% p.a

6% p.a

3% p.a

12% p.a

✅ Correct Option: 4

Given a present value of Rs. 2,50,000 which is equivalent to a perpetuity of Rs. 7,500 payable at the end of each quarter.

For a perpetuity, the present value formula is:

$PV = \dfrac{A}{r}$

where $PV$ is the present value, $A$ is the payment per period, and $r$ is the interest rate per period.

Substituting the known values:

$2,50,000 = \dfrac{7,500}{r}$

$r = \dfrac{7,500}{2,50,000}$

$r = 0.03$

This gives a quarterly interest rate of $3\%$ per quarter.

To convert the quarterly rate to an annual rate, multiply by the number of quarters in a year:

Annual Rate $= 3\% \times 4$

Annual Rate $= 12\%$ per annum

Therefore, the rate of interest is $12\%$ p.a.

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:

2026: 25 May Shift 1

The supply function for a commodity is $p = 3\sqrt{16+x}$ . If 9 units of goods are sold, then producer's surplus is :

2025: 15 May Shift 1

At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 20000?

2025: 30 May Shift 1

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

2024: 16 May Shift 1

For an investment, if the nominal rate of interest is $10 \%$ compounded half yearly, then the effective rate of interest is :

2026: 25 May Shift 1

A money-lender charges interest at the rate of 10 rupees per 110 rupees semi-annually, payable in advance. Then

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. rate per conversion period ( $i$ )	I. 2
B. nominal rate (r)%	II. 21
C. number of period in a year (m)	III. 20
D. effective rate of interest ( $r_e$ )%	IV. 0.1

Choose the correct answer from the options given below:

Solution