Insurance and Annuity Class 12 Commerce Maths 2 Chapter 2 Exercise 2.2 Answers Maharashtra Board
Balbharati Maharashtra State Board 12th Commerce Maths Digest Pdf Chapter 2 Insurance and Annuity Ex 2.2 Questions and Answers.
Std 12 Maths 2 Exercise 2.2 Solutions Commerce Maths
Question 1.
Find the accumulated (future) value of annuity of ā¹ 800 for 3 year at interest rate 8% compounded annually. [Given: (1.08)
3
= 1.2597]
Solution:
āµ C = ā¹ 800
āµ n = 3 years
āµ r = 8% p.a.
ā“ A = 10,000[(1.08)
3
ā 1]
ā“ A = 10,000[1.2597 ā 1]
ā“ A = 10,000 Ć 0.2597
ā“ A = ā¹ 2,597
Question 2.
A person invested ā¹ 5,000 every year in finance company that offered him interest compounded at 10% p.a., what is the amount accumulated after 4 years? [Given: (1.1)
4
= 1.4641]
Solution:
āµ C = ā¹ 5,000
āµ r = 10% p.a.
= 50,000[(1.1)
4
ā 1]
= 50,000[1.4641 ā 1]
= 50,000 Ć 0.4641
= ā¹ 23,205
Question 3.
Find the amount accumulated after 2 years if a sum of ā¹ 24,000 is invested every six months at 12% p.a. compounded half yearly. [Given: (1.06)
4
= 1.2625]
Solution:
āµ C = ā¹ 24,000
āµ n = 2 years
But invested half yearly
ā“ n = 2 Ć 2 = 4
āµ r = 12% p.a. compounded half yearly
= 4,00,000[(1.06)
4
ā 1]
= 4,00,000[1.2625 ā 1]
= 4,00,000 Ć 0.2625
= ā¹ 1,05,000
Question 4.
Find the accumulated value after 1 year of an annuity immediate in which ā¹ 10,000 are invested every quarter at 16% p.a. compounded quarterly. [Given: (1.04)
4
= 1.1699]
Solution:
āµ C = ā¹ 10,000
āµ n = 1 year
But invested every quarterly
ā“ n = 1 Ć 4 = 4
ā“ r = 16% p.a. compounded quarterly
= 2,50,000 [1.1699 ā 1]
= 2,50,000 Ć 0.1699
= ā¹ 42,475
Question 5.
Find the present value of an annuity immediate of ā¹ 36,000 p.a. for 3 years at 9% p.a. compounded annually. [Given: (1.09)
-3
= 0.7722]
Solution:
āµ C = ā¹ 36,000
āµ n = 3 years
āµ r = 9% p.a.
= 4,00,000 Ć 0.2278
= ā¹ 91,120
Question 6.
Find the present value of ordinary annuity of ā¹ 63,000 p.a. for 4 years at 14% p.a. compounded annually. [Given: (1.14)
-4
= 0.5921]
Solution:
āµ C = ā¹ 63,000
āµ n = 4 years
āµ r = 14% p.a.
= 4,50,000[1 ā 0.5921]
= 4,50,000 Ć 0.4079
= ā¹ 1,83,555
Question 7.
A lady plans to save for her daughterās marriage. She wishes to accumulate a sum of ā¹ 4,64,100 at the end of 4 years. What amount should she invest every year if she get an interest of 10%p.a. compounded annually? [Given: (1.1)
4
= 1.4641]
Solution:
āµ A = ā¹ 4,64,100
āµ n = 4 years
āµ r = 10% p.a.
ā“ 46,410 = C[1.4641 ā 1]
ā“ 46,410 = C Ć 0.4641
ā“ \(\frac{46,410}{0.4641}\) = C
ā“ C = ā¹ 1,00,000
Question 8.
A person wants to create a fund of ā¹ 6,96,150 after 4 years at the time of his retirement. He decides to invest a fixed amount at the end of every year in a bank that offers him interest of 10% p.a. compounded annually. What amount should he invest every year? [Given: (1.1)
4
= 1.4641]
Solution:
āµ A = ā¹ 6,96,150
āµ n = 4 years
āµ r = 10% p.a
ā“ 69,615 = C[1.4641 ā 1]
ā“ 69,615 = C Ć 0.4641
ā“ \(\frac{69,615}{0.4641}\) = C
ā“ C = ā¹ 1,50,000
Question 9.
Find the rate of interest compounded annually if an annuity immediate at ā¹ 20,000 per year amounts to ā¹ 2,60,000 in 3 years.
Solution:
āµ C = ā¹ 20,000
āµ A = ā¹ 2,60,000
āµ n = 3 years
ā“ 13i = 3i + 3 i
2
+ i
3
ā“ 13i = i(3 + 3i + i
2
)
ā“ 13 = 3 + i + i
2
ā“ i
2
+ 3i + 3 ā 13 = 0
ā“ i
2
+ 3i ā 10 = 0
ā“ (i + 5) (i ā 2) = 0
ā“ i + 5 = 0 or i ā 2 = 0
ā“ i = -5 or i = 2
āµ Rate of interest cannot be negative
ā“ i = 2 is accepted
ā“ \(\frac{r}{100}\) = 2
ā“ r = 200% p.a.
Question 10.
Find the number of years for which an annuity of ā¹ 500 is paid at the end of every years, if the accumulated amount works out to be ā¹ 1,655 when interest is compounded annually at 10% p.a.
Solution:
āµ C = 7500
āµ A = 71,655
āµ r = 10% p.a.
ā“ 0.331 + 1 = (1.1)
n
ā“ 1.331 = (1.1)
n
ā“ (1.1)
3
= (1.1)
n
ā“ n = 3 years
Question 11.
Find the accumulated value of annuity due of ā¹ 1,000 p.a. for 3 years at 10% p.a. compounded annually. [Given: (1.1)
3
= 1.331]
Solution:
āµ C = ā¹ 1,000
āµ n = 3 years
āµ r = 10% p.a.
ā“ Aā = 10,000 Ć 1.1[(1.1)
3
ā 1]
ā“ Aā = 11,000 [1.331 ā 1]
ā“ Aā = 11,000 Ć 0.331
ā“ Aā = ā¹ 3,641
Question 12.
A person plans to put ā¹ 400 at the beginning of each year for 2 years in a deposit that gives interest at 2% p.a. compounded annually. Find the amount that will be accumulated at the end of 2 years. [Given: (1.02)
2
= 1.0404]
Solution:
āµ C = ā¹ 400
āµ r = 2% p.a.
= 20,000 (1.02) (1.0404 ā 1)
= 20,400 [0.0404]
= ā¹ 824.16
Question 13.
Find the present value of an annuity due of ā¹ 600 to be paid quarterly at 32% p.a. compounded quarterly. [Given (1.08)
-4
= 0.7350]
Solution:
āµ C = ā¹ 600
āµ n = 1 year
ā“ But invested every quarterly
ā“ n = 1 Ć 4 = 4
āµ r = 32% p.a. compounded quarterly
= 7,500(1.08) [1 ā 0.7350]
= 8,100 [0.2650]
= ā¹ 2,146.5
Question 14.
An annuity immediate is to be paid for some years at 12% p.a. The present value of the annuity is ā¹ 10,000 and the accumulated value is ā¹ 20,000. Find the amount of each annuity payment.
Solution:
āµ r = 12% p.a.
ā“ i = \(\frac{r}{100}=\frac{12}{100}\) = 0.12
āµ P = ā¹ 10,000
āµ A = ā¹ 20,000
āµ \(\frac{1}{P}-\frac{1}{A}=\frac{i}{C}\)
ā“ C = 0.12 Ć 20,000
ā“ C = ā¹ 2,400
Question 15.
For an annuity immediate paid for 3 years with interest compounded at 10% p.a. the present value is ā¹ 24,000. What will be the accumulated value after 3 years? [Given (1.1)
3
= 1.331]
Solution:
āµ n = 3 years
āµ P = ā¹ 24,000
āµ r = 10% p.a.
ā“ i = \(\frac{r}{100}=\frac{10}{100}\) = 0.1
āµ A = P(1 + i)
n
ā“ A = 24,000 [1 + 0.1]
3
ā“ A = 24,000 Ć (1.1)
3
ā“ A = 24,000 Ć 1.331
ā“ A = ā¹ 31,944
Question 16.
A person sets up a sinking fund in order to have ā¹ 1,00,000 after 10 years. What amount should be deposited bi-annually in the account that pays him 5% p.a. compounded semi-annually? [Given: (1.025)
20
= 1.675]
Solution:
ā“ A = ā¹ 1,00,000
ā“ n = 10 years
But, invested half yearly
ā“ n = 10 Ć 2 = 20
āµ r = 5% p.a. compounded half yearly
ā“ r = \(\frac{r}{2}=\frac{5}{2}\) = 2.5%
ā“ i = \(\frac{r}{100}=\frac{2.5}{100}\) = 0.025
ā“ 2,500 = C[1.675 ā 1]
ā“ 2,500 = C Ć 0.675
ā“ \(\frac{2,500}{0.675}\) = C
ā“ C = ā¹ 3,703.70