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Numericals of Annuity

There are some theories and practical questions of annuity and deferred annuity for practice:

Questions:

1)      What is an annuity?
2)      What are the types of annuity?
3)      Give three point of difference between ordinary annuity and annuity due?
4)      What is Deferred Annuity? Explain with example.
5)      What are the types of deferred annuity?
6)      What is immediate annuity and variable annuity?
7)      What are the advantages and disadvantages of annuity?

8)      Suppose Mr. Nikhil has invested Rs. 6, 00,000 to his retirement plan. The insurance company gives interest of 8.2% semi-annually. Find out how much amount he will get after 8 years.

9)      Find out how much amount you will invest now in an annuity to get Rs. 60, 000 per month @ 7.9% quarterly for 7 years.

10)  Company XYZ equity offers 7 % annually return to his shareholders. After 3 years the profit of the company increases by 8%. So, the company decided to increase its return from 7% to 7.6% for 2 year only. The price of per share is Rs. 50. Mr. Sharma has purchased 10, 000 shares. Find out how much amount he will get after 5 years.

11)  Find out the future value of an annuity if monthly payment is Rs. 5, 000 and interest charged on 8.3% compounded annually for 4 years.

12)  Suppose Mr. Sharma has purchased 3 annuities whose monthly payments and other information are as follows:

Present value
Future Value
Monthly payments
years
3, 00,000
3, 90,000
42,000
5
1, 80,900
2,60,000
22,000
2
3, 60,700
3, 50,000
6, 000
6

Find out the rate of interest on all three annuities.

13)  Suppose you want to invest in a product on 1st January 2015 for an annuity @ 7% compounded quarterly for 5 years. The payment receives in 1st January 2019 at the beginning of each year. Find out present value of an annuity if the monthly payment receives is Rs. 10, 000.

14)  Find out the monthly payments if you purchase a washing machine worth Rs. 90, 000. The down payments value is Rs. 6, 000 and the interest charged on 6.3% annually. Company has fixed 9 instalments.

15)  Find out how much amount you will invest for 12 years to get 5, 000 per month at the beginning of the each month @ 7.5% compounded semi-annually. The beginning of payments receive is 4th year.

16)  Mr. Vikram has taken a loan of Rs. 3, 00,000 from bank to purchase a house. The interest rate charged by bank on loan is 8.2% compounded annually. He has to pay the amount in every end of the month. The payment of loan amount is starts from 3rd year from now for 12 years. Find out the monthly payment value.

17)  On January 2013 Company has decided to invest for yearly payment of Rs. 5, 000. But the receipt of the payment started from at the beginning of the 1st January 2017. The interest rate is 6.5 % compounded annually for 8 years. Find out the present value on 1st January 2016.

18)  Find out the present value of deferred annuity from the given information:   
                                                                                                    
Cash flows (in Rs.)
Rate of interest
Year
10, 000
5.9%
Cash flows started from 4th year from now.
10, 000


10, 000


10, 000


8, 000


8, 000




Answers:
8)  FV = 1, 141,203.05
9)  PV = 12, 81,021.62
10) FV = 2, 64,545
11) FV = 22, 630.639
12) i)  5.39%
ii)  19.88%
iii) -0.5%
13) PV = 1, 61,815.708
14)  13, 405.299
15)  PV = 72, 671.559
16) Pmt = 34, 356.512
17)  PV = 32, 422.598
18)  PV = 29243.1249 + 9832.923 = 39, 076.047



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