Statistics & Applications

Financial Math

Medium

applied

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. 40000?

10%

12%

✅ Correct Option: 2

A perpetuity is a series of payments that continue forever. The perpetuity pays Rs. 1,000 at the end of every 6 months, and its present value is Rs. 40,000.

The present value formula for a perpetuity is:

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

Where:

$PV$ = Present Value (Rs. 40,000)
$A$ = Payment amount (Rs. 1,000)
$r$ = Interest rate per period

Substituting the values:

$40,000 = \frac{1,000}{r}$

$r = \frac{1,000}{40,000}$

$r = 0.025$

$r = 2.5\%$

The rate of 2.5% is the interest rate per 6-month period, since payments occur every 6 months.

To convert to an annual rate:

Annual rate $= 2.5\% \times 2$

Annual rate $= 5\%$

Therefore, the rate of interest is 5%.

2025: 2 June Shift 1

A machine costing Rs 50,000 has a useful life of 4 years.The estimated scrap value is Rs 10,000 . The rate of depreciation per annum is:

2026: 18 May Shift 2

A car costing ₹ 5,00,000 has a useful life of 15 years. The estimated scrap value is ₹ 50,000. The annual depreciation using the straight line method is

2026: 22 May Shift 2

A person invested ₹2,00,000 in a mutual fund in year 2012. The value of the mutual fund increased to ₹3,00,000 in year 2017. The percentage of compound annual growth rate on the investment is:

(Given: $(1.5)^{1/5} = 1.084$ )

2025: 21 May Shift 2

A motorcycle has a scrap value of Rs. 22,500 after 15 years of its purchase. If the annual depreciation charge is Rs. 8,500, then the original cost by linear method is:

2025: 14 May Shift 2

Which of the following are NOT correct about "Sinking Fund"?

(A) It does not have any specific purpose.

(B) It can be used in any emergency.

(D) It is set up for a particular upcoming expense.

Choose the correct answer from the options given below:

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: $[given \, that(1.6)^{1/5} = 1.098]$

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. 40000?

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)