2 Marks Questions

Question 12 Marks

A machine can be purchased for ₹ 50000. Machine will contribute 12000 per year for the next five years. Assume borrowing is 10% per annum compounded annually Determine whether machine should be purchased or not.
Given P(5,0.1) = 3.79079

Answer

The present value of annual contribution $ P V=\text { C.F. } P(n, i) $
Here, C.F = ₹ 12000, $i=10 \%=\frac{10}{100}=0.10, n=5$
$\begin{array}{lrl}\text { and } & P(5,0.10) & =3.79079 \\ \therefore & P V & =12000 \times 3.79079\end{array}$
= ₹ 45489.48
which is less than the initial cost of the machine. Therefore machine must not be purchased.

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Question 22 Marks

ABC Ltd. wants to lease out an asset costing ₹ 36,000 for five years has fixed rental of ₹ 105000 per annum payable annually starting from the end of first year. Suppose rate of interest is 14% per annum compounded annually on which money can be invested by the company. Is this agreement favourable to the company ?
(Given, P(5,0.14) = 3.43308 )

Answer

First we have compute the present value of the annuity of 105000 for five years at the interest rate of 14% p.a. compounded annually. The present value PV of the annuity is given by
\[ =\text { C.F. } P(n, i) \]
Here, C.F. $=105000, i=14 \%=0.14, n=5$ and $P(n, i)=P(5,0.14)=3.43308$
$\therefore \quad P V=105000 \times 3.43308$
= ₹ 360473.40, which is greater than the initial cost ( ₹ 36, 0000) of the asset and consequently leasing is favourable to the lessor.

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Question 32 Marks

Write the relationship between present and future value of an annuity regular.

Answer

Present value of an annuity regular
$
=\frac{\text { Future value of an annuity regular }}{(1+i)^n}
$
Where, $i=$ is the rate of interest per conversion period
$n=$ no. of conversion period.

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Question 42 Marks

Write four applications of ordinary (regular) annuity.

Answer

Applications of regular annuity are:
(i) Leasing
(ii) Capital expenditure (investment decision)
(iii) Valuation of Bond
(iv) Sinking fund

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Question 52 Marks

What is the difference between annuity regular and annuity due?

Answer

Each payment of an ordinary (regular) annuity belongs to the payment period preceding its date, while the payment of an annuity-due refers to a payment period following its date.

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Question 62 Marks

Give four examples of regular annuity.

Answer

Examples of regular annuity are:
(i) Deposits to a saving account with regular period of time of a fixed payment.
(ii) Monthly insurance payments
(iii) Pension payments
(iv) Monthly rent of a house

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Question 72 Marks

Mr. Roy need to borrow money. His neighbourhood bank charges 8% interest compounded semi-annually. An internet bank charges 7.9% interest compounded monthly. At which bank will Mr. Roy pay lesser amount of interest ?

Answer

Compare effective rates:
Neighbourhood bank,
$\begin{aligned} E & =\left(1+\frac{0.08}{2}\right)^2-1 \\ & =0.0816=8.16 \%\end{aligned}$
Internet bank,
$E=\left(1+\frac{0.79}{12}\right)^{12}-1=0.08192=8.19 \%$
The neighbourhood bank has the lower effective rate although it has a higher nominal (actual) rate.1

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Question 82 Marks

Sachin deposited 100000 in his bank for 2 years at simple rate of 6%. How much interest would he earn? How much would be the final value of deposit ?

Answer

Required interest amount is given by
$\begin{aligned} I & =\text { Pit } \\ & =100000 \times \frac{6}{100} \times 2\end{aligned}$
Final value of deposit is given by
$A=P+I$
= ₹ (100000 + 12000)
= ₹ 112000.

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