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Model Paper 10 — Applied Maths STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsModel Paper 104 Marks
Question
Read the text carefully and answer the questions:
Understanding Perpetuity
An annuity is a stream of cash flows. A perpetuity is a type of annuity that lasts forever, into perpetuity. The stream of cash flows continues for an infinite amount of time. In finance, a person uses the perpetuity calculation in valuation methodologies to find the present value of a company's cash flows when discounted back at a certain rate.
An example of a financial instrument with perpetual cash flows was the British-issued bonds known as consols, which the Bank of England phased out in 2015. By purchasing a consol from the British government, the bondholder was entitled to receive annual interest payments forever.
Perpetuity Present Value Formula
The formula to calculate the present value of perpetuity or security with perpetual cash flows is as follows:
$PV =\frac{C}{(1+r)^1}+\frac{C}{(1+r)^2}+\frac{C}{(1+r)^3} \cdots=\frac{C}{r}$
where:
PV present value
C = cash flow
r = discount rate
(a) Find the present value of a perpetuity of ₹ 900 payable at the end of each year, if money is worth 5% per annum.
(b) Find the present value of a perpetuity of ₹ 500 payable at the end of each quarter, if money is worth 8% per annum.
(c) Find the present value of a perpetuity of ₹ 300 payable at the beginning of every 6 months, if money is worth 6% per annum.
✓

Answer

Read the text carefully and answer the questions:
Understanding Perpetuity
An annuity is a stream of cash flows. A perpetuity is a type of annuity that lasts forever, into perpetuity. The stream of cash flows continues for an infinite amount of time. In finance, a person uses the perpetuity calculation in valuation methodologies to find the present value of a company's cash flows when discounted back at a certain rate.
An example of a financial instrument with perpetual cash flows was the British-issued bonds known as consols, which the Bank of England phased out in 2015. By purchasing a consol from the British government, the bondholder was entitled to receive annual
interest payments forever.
Perpetuity Present Value Formula
The formula to calculate the present value of perpetuity or security with perpetual cash flows is as follows:
$PV =\frac{C}{(1+r)^1}+\frac{C}{(1+r)^2}+\frac{C}{(1+r)^3} \cdots=\frac{C}{r}$
where:
PV present value
C = cash flow
r = discount rate
(i) ₹ 18000
(ii) ₹ 25000
(iii)₹ 10300

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