Statistics & Applications

Financial Math

Medium

applied

At what rate of interest will the present value of a perpetuity of ₹ 500 payable at the end of every 6 months be ₹ 20,000?

10% per annum

20% per annum

5% per annum

7% per annum

✅ Correct Option: 3

The payment received is ₹500 every 6 months and the present value is ₹20,000.

For a perpetuity, the present value formula is:

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

Rearranging:

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

Since the payment is every 6 months, the rate calculated will be for a 6-month period.

Rate per 6 months $= \dfrac{500}{20,000}$

Rate per 6 months $= 0.025$

Rate per 6 months $= 2.5\%$

There are 2 six-month periods in a year.

Annual Rate $= 2.5\% \times 2$

Annual Rate $= 5\%$ per annum

Therefore, the rate of interest is 5% per annum.

2026: 12 May Shift 2

Which of the following approaches is not associated to valuation of bonds ?

2024: 16 May Shift 1

A flower vase costs ₹ $36,000$ . With an annual depreciation of ₹ $2,000$ , its cost will be ₹ $6,000$ in $_____$ years.

2026: 30 May Shift 2

Scrap value of a machine is one-tenth of its actual cost. If the estimated life of the machine is ten years and the annual depreciation under linear method is ₹45000, then the cost of the machine is

2026: 29 May Shift 1

Which of the following are correct?

(A) Sinking fund is a fixed term account.

(B) Sinking fund is set-up for a particular upcoming expense.

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

Choose the correct answer from the options given below:

2026: 21 May Shift 1

A bike costs ₹85,000 and has a useful life of 15 years. If the scrap value of the bike after 15 years is ₹10,000, then the book value of the bike at the end of the tenth year is

2026: 21 May Shift 2

Renu takes a loan of ₹12,00,000 with 12% annual interest for 10 years on flat rate basis..

Match the LIST-I with LIST-II

LIST-I		LIST-II
A. Principal of the loan		I. ₹14,40,000
B. Total interest on the principal		II. ₹26,40,000
C. EMI		III. ₹12,00,000
D. Total amount paid in 10 years		IV. ₹22,000

Choose the correct answer from the options given below:

At what rate of interest will the present value of a perpetuity of ₹ 500 payable at the end of every 6 months be ₹ 20,000?

Solution

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