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Published on: 13/05/2022

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Questions:

Generic 2

5 x 2 = 10

Find the amount of annuity of Rs. 2000 payable at the end of each year for 4 years of money is worth 10% compounded annually [(1.1)⁴ = 1.4641]

Find the number of shares which will give an annual income of Rs. 3,600 from 12% stock of face value Rs. 100.

Find the market value of 325 shares of amount Rs. 100 at a premium of Rs. 18.

What is the present value of an annuity due of Rs. 1,500 for 16 years at 8% per annum? [(1.08)^-16 = 0.2919]

Find the amount of an ordinary annuity of Rs. 3,200 per annum for 12 years at the rate of interest of 10% per year. [(1.1)¹² = 3.3184]

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Answers Key:

Generic 2

5 x 2 = 10

a = Rs. 2000; i =10% = 0.1 n = 4
A = \(\cfrac { a }{ i } \left[ \left( 1+i \right) ^{ n }-1 \right] \)
\(=\frac { 2000 }{ 0.1 } \left[ (1+0.1)^{ 4 }-1 \right] \)
= 20,000[ 1.464-1]
= 20,000 (0.464)
A = Rs. 9280

Let ‘x’ be the number of shares.
Face Value = Rs. 100
Face value of ‘x’ shares = Rs. 100x
\(\frac{12}{100}\times 100x=Rs. 3600\)
12 x = 3600 \(\Rightarrow\) x = 300
Hence the number of shares = 300

Face value of a share = Rs. 100
Premium per share = Rs. 18
M.V. of a share = Rs. 118
Market value of 325 shares = number of shares × M.V of a share
= 325 × 118 = Rs. 38,350
Therefore market value of 325 shares is Rs. 38,350.

a = Rs.1500, i = \(\frac{8}{100}\) = 0.08, n = 16
P = \(\cfrac { a\left( 1+i \right) }{ i } \left[ 1-\cfrac { 1 }{ \left( 1+i \right) ^{ n } } \right] \)
=\(\cfrac { 1500\left( 1.08 \right) }{ 0.08 } \left[ 1-\cfrac { 1 }{ \left( 1.08 \right) ^{ 16 } } \right] \)
\(=\cfrac { 1500 \times 1.08}{ 0.08 } \left[ 1- { \left( 1.08 \right) ^{ -16 } } \right] \)
= 20250 [1 - 0.2919]
= 20250 [0.7081]
= Rs.14339

A = \(\cfrac { a }{ i } \left[ \left( 1+i \right) ^{ n }-1 \right] \)
Where a = Rs. 3,200, n = 12, i = \(\cfrac{10}{100}\) = 0.1
\(A=\cfrac { 3200 }{ 0.1 } \left[ \left( 1+0.1 \right) ^{ 12 }-1 \right] \)
\(\left[ \because \left( 1.1 \right) ^{ 12 }=3.1384 \right] \)
= 32,000 [3.1384 - 1] = 32,000 x 2.1384
= Rs. 68428.8
≈ Rs. 68429