Rajat is considering various retirement planning and savings scenarios. He wants to know how much to save and invest annually over different time periods to achieve goals such as accumulating Rs. 5 million by retirement age 65, having funds to withdraw Rs. 1 million annually in retirement until age 90, and donating Rs. 200,000 every 5 years until age 75. A financial planner helps calculate the required annual contribution amounts for Rajat to meet his objectives given expected rates of return.

1. Planning for Savings,
Spending, and Annuity
Arindam Banerjee
CFP FCMA
arindam20011@gmail.com

2. 1
‘A’ promises to pay ‘B’ a sum of Rs. 20000
at the end of 3 years and another Rs.
40000 at the end of 5 years from now. What
cash amount should be accepted now in
lieu of the above two payments if interest is
5% p.a?

3. 2
An employee aged 35 years invested Rs.
10000 in a savings instrument. The interest
during the first 5 years is 8% pa and
thereafter 6% pa. What amount would he
get on retirement at the age of 58 years?

4. 3
A person purchases a money back policy at
the age of 32 years. He gets Rs. 50000
each at the end of 5, 10, and 15 years as
survival benefits and a sum of Rs. 200000
on maturity at the end of 20 years. He
invested all these payments at 6% pa. What
is the accumulated amount available to him
on retirement at the age of 60 years?

5. 4
The cash purchase price of a car is Rs.
200000. A company, however, offers
instalment plan where under an immediate
payment of Rs. 40000 is to be made and a
series of 5 half yearly payments made
thereafter. The first instalment is payable
after 6 months. If the company wishes to
realize a rate of interest of 10% convertible
half yearly, calculate the half yearly
instalment.

6. 5
Calculate the present value of an immediate
annuity payable for 20 years certain at the
rate of 15000 pa. The first instalment being
due at the end of one year. Assume rate of
interest as 7% pa.

7. 6
What would be the PV at a rate of interest of
5% pa of a deferred annuity payable for 10
years certain, the first instalment falling due
at the end of 6 years from now. The annuity is
payable at the rate of Rs. 100000 pa for the
first 5 years and Rs. 200000 for the next 5
years.

8. 7
A sum of Rs. 50000 is invested at a rate of
interest of 5% pa. After 7 years, the rate of
interest was changed to 5% pa convertible
half yearly. After a further period of 3 years,
the rate was again changed to 6% pa
convertible quarterly. Find the accumulated
amount at the end of 15 years from
commencement.

9. 8
Find the rate of discount corresponding to a
rate of interest of 6% pa.

10. 9
Which yields the higher rate of interest for
every Rs. 1000 in a bank or an NSC giving
the following maturity values respectively?
a) Rs. 1629 after 5 years in a Bank FD
b) Rs. 1901 after 6 years in NSC

11. 10
Ms. Ritu deposited a sum of Rs. 2500000 in an
annuity certain plan for 25 years providing a
yield of 6% pa. What would be the amount
of annuity if she wishes to receive annual
annuity payments:
a) Payable in arrears
b) Payable in advance

12. 11
Mr. Vijay got a sum of Rs. 1000000 on
retirement. He spends Rs. 100000 on
renovation of his house, Rs. 200000 on a
new car and keeps Rs. 200000 as reserve for
emergencies. The balance amount is
invested at 8% pa in a plan allowing
withdrawal of Rs. 50000 at the end of each
year. How long his money will last in the said
plan?

13. 12
Ashok, a middle level executive, aged 45 years saves
at 9% pa Rs. 200000 in the beginning of a year for
the first 8 years and then stops saving on account of
certain financial contingencies. On retirement at the
age of 65 years, he intends to keep aside a sum of
Rs. 500000 out of the accumulated amount of the
above savings as liquid money for emergencies and
to invest the balance amount at 6% pa providing
withdrawal of a fixed amount at the end of every
year for 20 years. Find the amount of annual
withdrawals.

14. 13
Under an educational loan, a person receives
four annual installments of Rs. 10000 each,
the first payment being made at the present
moment. The loan is to be repaid in lump
sum at the end of 10 years from now along
with 6% interest pa. Calculate the amount
repayable.

15. 14
An employee aged 25 years is currently spending Rs.
100000 pa. If the rate of inflation is 5% and he
wishes to maintain the present standard of living
throughout his life. What amount would he be
requiring to spend during the first year of his exit
from service if the retirement age is
a) 55 years
b) 58 years
c) 60 years
d) 65 years

16. 15
Mohan aged 30 years is working in an MNC and wishes to set aside
some fixed amount at the beginning of each year towards
retirement planning. He is currently spending Rs. 240000 pa and
wishes to raise his standard of living by 2% per year until his
retirement age at 55 years. The average rate of inflation is
expected to be 3% all these years. If he wants to maintain 90%
of his standard of living that he would be enjoying on retirement
assuming no provision for inflation thereafter, then what is the
annual amount of income he should manage for after retirement?

17. 16
In the previous case, if Mohan’s life expectancy
on retirement is 25 years and he wants the
same annual income as envisaged in
previous case for all the years in advance
after retirement. What accumulated amount
should he have on retirement for such an
arrangement? Assume the discounting rate is
6% pa

18. 17
John aged 42 years working in a software
company wants “nest eggs” amounting to
Rs. 5000000 at his retirementage of 65
years. Assume rate of interest 10% p.a.
a) How much amount should he save in the
beginning of every year until retirement?
b) Alternatively, how much amount should he
save at the end of every year until
retirement?

19. 18
An employee aged 57 years wishes to purchase an
annuity certain for 20 years starting from age 60 by
paying single premium. Calculate the single
premium payable now. The amount of annual
annuity payment is Rs. 100000. First instalment is
paid at the end of 3 years and remaining at 1 year
intervals thereafter. Assume interest to be 7 % pa
during the deferment and the annuity payment
period.

20. 19
A has invested Rs. 1000 in a savings
instrument maturing after 15 years. On its
maturity, he receives a sum of Rs. 1750.
What rate of interest is realised in this
transaction?

21. 20
Ram is aged 32 years and would retire at the age of
60 years. He deposits 8% of his annual salary in his
pension account at the end of the year. What will be
his annual pension account at the end of the year of
retirement. What will be his annual pension amount
paid to him at the start of the year on retirement.
Rate of interest is 6% pa. Pensions stop when Ram
turns 75 years.
# Salary will be 450000 between ages 32 to 40
# 550000 between ages 40 to 50
# 600000 between 50 to 60

22. 21
Find PV of an annuity certain that pays 50000
at the end of the year for next 10 years,
70000 for next 10 years and 80000 for the
last 10 years. Assume rate of interest to be
6% pa for 20 years and 5% pa for the last 10
years.

23. 22
Meera deposits Rs. 200000 in an account, then
starts withdrawing level annual payments
starting 1 year after the deposit was made. If
immediately after 11th drawing, she has Rs.
40000 left in her account. Find the amount of
each cash withdrawal if annual rate of
interest is 8%

24. 23
Suppose you have an opportunity to make an
investment in a real estate venture that expects
to pay investors Rs. 750 at the end of each
month for the next eight years. You believe that
a reasonable return on your investment should
be 17% p.a compounded monthly.
# How much should you pay for the investment?

25. 24
Rajat considering the purchase of an
apartment for Rs. 100000. They estimate that
they will receive Rs. 15000 at the end of each
year for the next 10 years. At the end of 10th
year, the apartment project will be worth
nothing. If Rajat purchases the project, what
will be the internal rate of return?

26. 25
Dinesh is considering the purchase of an
investment that is expected to generate cash
flows of Rs. 15000 per year for the next 5
years. After that, cash flows are expected to
increase at the rate of 5% per year for the
indefinite future. How much is this investment
worth to Dinesh today, if the required return is
15%?

27. 26
Rajat plans to retire in 15 years. After retire
Rajat will need Rs. 500000 pa. Rajat thinks
he will live 10 years after retirement. Taking
interest rate at 8%, how much he will need to
accumulate till retirement?

28. 27
Rajat wishes to invest in an ICICI bond that
pays interest quarterly. ICICI wish to pay
effectively 16% p.a on this bond. Rajat
wishes to know the annual percentage rate
(APR) on this bond rather than the effective
interest rate. What is the APR that
corresponds to an effective rate of 16% for
this bond?

29. 28
Rajat plans to retire 33 years from now. He expects to live 27
years after retirement. He wants to have enough money upon
reaching retirement age to withdraw Rs. 1000000 p.a from the
account at the beginning of each year he expects to live, and
yet still have Rs. 5000000 left in the account at the time of
expected death (60 years from now). He plans to accumulate
the retirement fund by making equal annual deposits at the
end of each year for the next 33 years. Rajat expects that he
will be able to earn 12% p.a till retirement. However, after
retirement he expects only to earn 6% p.a on investments.
How much Rajat should invest each year to achieve his goal?

30. 29
Rajat wants to set aside an equated monthly
amount from today for a family foreign trip
costing Rs. 800000 now. A travel company is
offering a customized solution for this to Rajat.
As per the offer, after 2 years the company will
bear the total travel cost at the then prices and
Rajat shall have to pay the cost at 60 EMIs,
charging nominal interest rate of 10% p.a
(compounded monthly), EMI starting from today.
Rajat wants to know how much EMI he will have
to pay for this arrangement. (Inflation rate is 15%
p.a)

31. 30
Rajat (aged 40years with life expectancy 75
years) wants to donate Rs. 200000 (the then
value) to an NGO on each of the last 5
birthdays of his life. As a financial planner you
advised him to invest a fixed amount on
every birthday (starting from his next
birthday) in 22 instalments in an 8% p.a
yielding investment. What annual amount
should he contribute to ensure donation as
per his plan?