Exercises – Annuity
1. Find the amount of an ordinary annuity of
a. Rs. 500 payable at the end of each year for 7 years at 7% interest rate p.a. [Rs. 4327.01]
b. Rs. 500 made at the end of each quarter for 10 years at 8% p.a compounded quarterly. [Rs. 30,201]
c. 12 monthly payments of Rs. 1000 that earn interest @ 12% p.a. compounded monthly. [Rs 12682.50]
d. Rs. 500 payable at the each year for 14 years if money is worth 5% compounded annually. [Rs. 9799.31]
2. To save for a child’s education, a family decides to invest Rs. 3000 at the end of each 6-month period in a fund
paying 8% per year compounded semi-annually. Find the amount of the investment at the end of 18 years. [Rs.
232794.94]
3.
4.
A man deposits Rs 5000 at the end of every 2 months for five years. He made his first payment on 28th February
2010 and the last payment on 31st December 2014. How much should be there on 31st December 2014, if the
rate of interest is 10% p.a. compounded every 2 months? [Rs. 192582.29]
If a person wants to accumulate Rs. 50000 by making equal payments at the end of each quarter for the next
five years, what will be the size of these investments if money is worth 6% p.a. compounded quarterly? [Rs.
2162.28]
A man wants to have Rs. 12000 in his account after 10 years. He deposits annual payments in an account that
pays 4% rate of interest compounded annually. How much should he deposit at the end of each year? [Rs. 999.49]
6. A machine costs Rs. 98000 and its effective life is estimated to 12 years. If the scrap value is Rs 3000 only, what
should be retained out of profits at the end of each year to accumulate at compound interest at 5% p.a. for
depreciation so that a new machine of the same type can be purchased after 12 years? Assume average
inflation rate of 3% p.a. for the next 12 years. [Rs. 8589.77]
7. A company sets aside a sum of Rs. 5000 annually at the end of each year for 10 years to pay off a debenture
issue of Rs. 60000. If the fund accumulates at 5% per annum compound interest, find the surplus after full
redemption of the debenture issue? [Rs. 2889.46]
8. Find the least number of years for which an annuity of Rs. 1500 per annum must run in order that its amount
just exceeds Rs. 30000 at 9% compounded annually. [12 years]
9. Find the present value of an ordinary annuity of
a. Rs. 5000 per annum for 12 years @ 4% p.a. compounded annually. [Rs. 46925.37]
b. 24 payments of Rs. 100 each made monthly @ 9% p.a. compounded monthly. [Rs. 2188.91]
c. Rs. 800 payable at the end of each 6 months for 5 years, if money is worth 6% compounded semi-annually.
5.
[Rs. 6824.16]
10. A man retires at the age of 60 years and his employer gives him a pension of Rs 50000 per year at the end of
every year for the rest of his life. Reckoning his expectation of life to be 13 years and that interest is at 7% per
annum, what single sum is equivalent to his pension? [Rs. 417882.54]
11. A fixed royalty of Rs 1000 per year is granted to an author by the publisher of a book for 20 years. The author
decides to sell his right of receiving the royalty after 12 years. Assuming money is worth 12% p.a., at what price
should the author sell his right? [Rs. 4967.64]
12. A man buys a machine on instalment basis such that he pays Rs. 10000 on signing of the contract and remaining
in 4 equal monthly instalments of Rs. 5000 each made at the end of every month. The rate of interest is 12%
p.a. compounded monthly. His friend wants to buy the machine on full-cash basis. How much would it cost him?
[Rs. 29510]
13. Mr Sukumar takes a loan of Rs. 25 lakh on 1st January 2010 at an interest rate of 8.5% p.a. He agrees to repay
the loan in 60 equal monthly instalments starting from 31st January 2011. How much would be the EMI? [Rs.
55651.09]
14. Mr Sadiq wants to invest some amount at the end of every month for the next 30 years till his retirement so
that he can receive Rs. 20000 at the end of every month after his retirement for the next 20 years. The relevant
rate of interest is 9% p.a. How much should he save every month to meet his objective? [Rs.1214.20]
15. Mr Mahesh has Rs. 25 lakh in his pension account. The pension account starts giving him a fixed amount at the
end of every month for the next 15 years. The relevant rate of interest is Rs. 8%. However, Mr Mahesh decides
to close the account and receive in full the balance amount at the end of 5 years. What will Mahesh get? [Rs.
1969156.33]
16. How much will 12 annuities of Rs. 10000 per month starting from 1st January amount to on 31st December if the
prevailing interest rate is 12% p.a.? [Rs. 128093.28]
17. Mr. Mubarak opens a 9.5% recurring deposit account with the bank with Rs. 5000 and commits to deposit Rs.
5000 every month for 5 years. How much would be the balance in his account at the end of the 5 year period?
[Rs. 385136.29]
18. Calculate the sum of annuity due of
a. Rs. 500 paid every year for 10 years at the rate of 10% p.a. [Rs. 8765.58]
b. Rs. 500 paid every month for 5 years at the rate of 6% p.a. compounded monthly. [Rs. 35059.44]
c. Rs. 500 paid every quarter for 4 years at the rate of 8% p.a. compounded quarterly. [Rs. 9506.04]
19. You buy a motorbike by agreeing to pay for it in 24 equal monthly instalments of Rs. 2000 starting from the date
of purchase. The rate of interest used to calculate the size of the instalment is 14%. What is the cash down price
of the bike? [Rs. 42141 approx]
20. Calculate the present value of an annuity due of
a. Rs. 1000 paid every 2 months for 10 years at the rate of 10% p.a. compounded every 2 months. [Rs. 38373.63]
b. Rs. 1000 paid every year for 10 years at the rate of 11% p.a. [Rs. 6537.05]
21. Mr. Sashi buys a vehicle on January 1st 2012 with a down payment of Rs. 10000 and agrees to pay the remaining
amount in 24 equal monthly instalments of Rs. 2000 each payable on the 1st of every month starting from June
1st 2012. What is the price of the vehicle if the effective rate of interest is 12%? [Rs. 50868 approx]
22. Arjun purchases a house from Bashir and agrees to pay Bashir twenty annual instalments of Rs. 20000 each, the
first to be paid immediately. If money is worth 8% effective, what is the equivalent cash price of this house? [Rs.
212072]
23. An annuity consists of 5 annual payments of Rs. 1000 each, the first being made at the end of 4 years. Find the
amount of this annuity if money is worth 8% effective. [Rs. 5866.60]
24. Find the amount of a sequence of annual payments of Rs. 6000 each, the first being made at the end of 6 years,
and the last at the end of 10 years, if money is worth 5% effective. [Rs. 33153.79]
25. Raghu buys a piece of land for which he agrees to make 10 annual payments of Rs. 20000 each, the first being
made at the end of 3 years. Find the equivalent cash price of this property if money is worth 5% effective. [Rs.
140077]
26. Mathews borrowed Rs. 50000 at compound interest of 7% p.a. and has to repay the money in 20 equal yearly
instalments. What should be the instalment if repayment has to start 3 years hence? [Rs. 5403.52]
27. How much should a company set aside at the end of each year if it has to buy a machine expected to cost Rs.
200000 at the end of 6 years and the rate of interest is 10% p.a. compounded annually? [Rs. 25921.47]
28. A machine costs a company Rs. 52000 and its effective life is estimated at 25 years. A sinking fund is created for
replacing the machine by a new model at the end of its life time, when its scrap realises a sum of Rs. 2500 only.
The price of the new model is estimated to be 25% more than the price of the present one. Find the amount
that should be set aside at the end of each year for the sinking fund, if it accumulates at 3.5% p.a. compound?
[Rs. 1604.63]
29. How much should you save at the beginning of every month for the next 15 years so that you will get back Rs.
20000 at the beginning of every month from the 16th year onwards for the next 20 years? Assume relevant rate
of interest to be 12% p.a. [Rs. 3635.83]
30. You have taken a loan of Rs. 5 lakh from the bank @ 18% p.a. You commit to repay the loan in 60 equal monthly
instalments starting after 1 year. How much will the instalment be? [Rs. 14760.61]