Statistics & Applications

Financial Math

Medium

applied

At what rate will the present value of a perpetuity of Rs.1000 payable at the end of each quarter be Rs.50000?

5% p.a

8% p.a

2% p.a

4% p.a

✅ Correct Option: 2

Given:

Payment amount = Rs. 1,000 (paid every quarter)
Present Value = Rs. 50,000
Payment frequency = Quarterly

A perpetuity is a series of payments that continues forever.

For a perpetuity:

Present Value $= \dfrac{\text{Payment per period}}{\text{Interest rate per period}}$

Rearranging:

Interest rate per period $= \dfrac{\text{Payment per period}}{\text{Present Value}}$

Since payments happen every quarter, the quarterly rate is:

Quarterly rate $(r) = \dfrac{1,000}{50,000}$

$r = 0.02$

$r = 2\%$ per quarter

Since there are 4 quarters in a year:

Annual rate $= \text{Quarterly rate} \times 4$

Annual rate $= 2\% \times 4$

Annual rate $= 8\%$ per annum

Therefore, the interest rate is 8% p.a.

2026: 12 May Shift 2

Rama takes a personal loan for a car worth ₹5,00,000 at an interest rate of 7% per annum to be repaid by equal monthly instalments (EMI) in 5 years. Using flat rate method, EMI will be:-

2025: 22 May Shift 2

Anush takes a loan of ₹ 150000 @ 16% annual interest for 5 years. His EMI (Equally Monthly Installment) on monthly basis under flat rate system is:

2026: 31 May Shift 2

Ankur takes a personal loan of ₹ 3,00,000 at the rate of 12% per annum for two years. His EMI using a flat rate method will be:

2025: 21 May Shift 1

Which of the following statements are correct?

(A) In the sinking fund a fixed amount at regular intervals is deposited.

(B) Sinking fund is a long-term account which can be closed any time.

(D) Sinking fund can be used only for the purpose it was created.

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: 30 May Shift 1

If an investment value get doubled in 10 years then its compound annual growth rate (CAGR) is: (Given $2^{1/10} = 1.0729$ )

At what rate will the present value of a perpetuity of Rs.1000 payable at the end of each quarter be Rs.50000?

Solution

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