Q1.
The present value of an annuity Rs.3000 for 15 years at 9.5% p.a. C.I. is
(a) 23484.5 (b) 20,000 (c) 32,000
(d) 28486.5
Solution.
P =
c/i
[
(1 + i)n - 1/(1 + i)n
]
P =
3000/0.095
[
(1 + 0.095)15 - 1/(1 + 0.095)15
]
P = (31,579) [
3.901322 - 1/3.901322
]
P = (31,579) [
2.901322/3.901322
]
P = (31,579)(0.743677)
P = 23,484.5
Solution
Q2.
A machine can be purchased for Rs.50,000 . Machine will contribute Rs.12000 per year for the next five years. Assume borrowing cost is 10%
per annum. What is the present value of contribution.
(a) 40,000 (b) 45,490 (c) 52,600 (d) 48,640
Solution.
P =
c/i
[
(1 + i)n - 1/(1 + i)n
]
P =
12000/0.1
[
(1.1)5 - 1/(1.1)5
]
P = 120000
[
1.61051 - 1/1.61051
]
P = 120000
[
0.61051 /1.61051
]
P = 120000(0.379079)
P = 45,489.5
Solution
Q3.
Find the future of an annuity of Rs.1000 made annuity for 10 years at interest rate of 14% compounded annually.
(a) 19,337 (b) 21,109 (c) 45,763 (d) 19,999
Solution.
A =
c/i
[(1 + i)
n - 1]
A =
1000/0.14
[(1 + 0.14)
10 - 1]
A = 7142.8[(1.14)
10 - 1]
A = 7142.8(3.707221 - 1)
A = 7142.8(2.707221)
A = 19337
Solution
Q4.
A person purchased a car of Rs. 750000. He made down payment of Rs.250000. Rest amount he wish to repay in 12 equal monthly instalments
with interest 15% p.a. compute instalment amount.
(a) 40000 (b) 30000 (c) 45130 (d) 44890
Solution.
P =
c/i
[
(1 + i)n - 1/(1 + i)n
]
500000=
c/0.0125
[
(1 + 0.0125)12 - 1/(1 + 0.0125)12
]
effective(r) =
r/12
=
15/12
= 1.25
i =
effective(r)/100
=
1.25/100
= 0.0125
C = 45,130
Solution
Q5.
A luxary is purchased for Rs.500000 cash down and Rs.30000 per month for 3 years . Find the cash price of the luxary car if the payment
include interest at 12% compounded monthly?(1.01)36 = 1.43077
(a) Rs.1540860 (b) Rs.16 lac. (c) Rs.1403227/-
(d) Rs. 17 lac.
Solution.
Cash prices of the car = Amount of cash down payment + present value of the annuity
Annuity (c) = 30000
n =
3 years = 3 x 12 = 36
effective rate of interest (re) =
r/12
%
=
12/12
%
i =
re/100
=
1/100
= 0.01
P =
c/i
[
(1 + i)n - 1/(1 + i)n
]
P =
30000/0.01
[
(1 + 0.01)36 - 1/(1 + 0.01)36
]
P = 3000000 [
(1.01)36 - 1/(1 + 0.01)36
]
P = 3000000 [
1.43077 - 1/1.43077
]
P = 903227
cash price of the car = 500000 + 903227
P = Rs.1403227
Solution
Q6.
A company may obtain a machine either by leasing it for 5 years (useful life) at an annual rent of Rs.4000/- or by purchasing the machine
for Rs.15600/-. If the company can borrow money at 18% per annum, which alternativeis preferable ?
(a) Purchasing (b) leasing (c) can't say (d) none of these
Solution.
(b) leasing
→ In this case there are option either purchase the machine or leasing .
→ In the case
of purchase, company will expend Rs.15600 .
→ In the case of leasing , company will pay Rs.4000 per annum upto 5 years.
Now , find present value of these five payments.
C = 4000, n = 5 ,
r = 18% , i =
r/100
=
18/100
= 0.18
P =
c/i
[
(1 + i)n - 1/(1 + i)n
]
P =
4000/0.18
[
(1 + 0.18)5 - 1/(1 + 0.18)5
]
= Rs.12,509
→ Total leasing expenditure is less than purchase .
Solution
