The document discusses the concepts of time value of money including compound interest, future value, present value, and annuities. It provides examples and explanations of how to calculate future value, present value, and payments for annuities using formulas and the Excel functions FV, PV, PMT, NPER, and RATE. It also includes sample problems and exercises for readers to practice these time value of money calculations.

2. • “RM today is worth more than a RM
tomorrow”
• You can take that RM today……
• and invest it with the expectation to
having more than a RM tomorrow

3. The Time Value of Money
• What is the “Time Value of Money”?
• Compound Interest
• Future Value
• Present Value
• Annuities
• PMT(Payment)

4. Obviously, RM1,000 todayRM1,000 today.
Money received sooner rather than later allows one
to use the funds for investment or consumption
purposes. This concept is referred to as the TIMETIME
VALUE OF MONEYVALUE OF MONEY!!
Which would you rather have - RM1,000 todayRM1,000 today
or RM2,000 in 3 years?RM2,000 in 3 years?
The Time Value of Money

5. How can one compare amounts
in different time periods?
• One can adjust values from different time
periods using an interest rate.
• Remember, one CANNOT compare
numbers in different time periods
without first adjusting them using an
interest rate.

6. Compound Interest
When interest is paid on not only the principal amount
invested, but also on any previous interest earned, this
is called compound interest.
FV = Principal + (Principal * Interest)
= 1000 + (1000 * .10)
= 1000 (1 + i)
= PV (1 + i)
= 1100
Note: PV refers to Present Value or Principal

7. If you invested RM100 today in an account that pays 10%RM100 today in an account that pays 10%
interest, with interest compounded annually, how much will
be in the account at the end of two years if there are no
withdrawals?
Future Value (Graphic)
0 1 2
RM100RM100
FVFV
10%

8. FVFV11 = PVPV (1+i)n
= RM100RM100 (1.10)2
= RM121RM121
Future Value (Formula)
FV = future value, a value at some future point in time
PV = present value, a value today which is usually designated as time 0
i = rate of interest per compounding period
n = number of compounding periods

9. •Excel makes these calculations easy with the use of theExcel makes these calculations easy with the use of the
built-in functionbuilt-in function FV:FV:
FV(Rate,Nper,PMT,PV,FV(Rate,Nper,PMT,PV,TypeType))
•There are five parameters to theThere are five parameters to the FVFV function.function.
•RateRate :: is the interest rate per period (year, month, day, etc)is the interest rate per period (year, month, day, etc)
•NperNper :: is the total number of periodsis the total number of periods
•PVPV :: is the present valueis the present value
•PMTPMT andand TypeType are included to handle annuities (a series ofare included to handle annuities (a series of
equal payments, equally spaced over time)equal payments, equally spaced over time)
** will be discussed later. For problem of the type that we are currently solving,will be discussed later. For problem of the type that we are currently solving,
we will set both PMT andwe will set both PMT and TypeType to 0.to 0.
Future Value (Microsoft Excel)

10. •We want to calculate the future value of RM100, for two
years at 10% per year.
•The result is RM121.
•Note we have entered –B1 for the PV parameter.
•The reason for the negative sign is that Excel realizes that
either the PV or FV must be a cash flow.
*if we had not used the negative sign, the result (FV) would have been negative.
Future Value (Microsoft Excel)

11. Ahmad wants to know how large his RM5,000RM5,000 deposit will
become at an annual compound interest rate of 8% at the
end of 5 years5 years.
Future Value Example
0 1 2 3 4 55
RM5,000RM5,000
FVFV55
8%

12. Present Value
• Since FV = PV(1 + i)n.
PVPV = FVFV/(1+ i)n.
• Discounting is the process of translating a
future value or a set of future cash flows into
a present value.

13. Assume that you need to have exactly RM1210RM1210 saved 2
years from now.years from now. How much must you deposit today in an
account that pays 10% interest, compounded annually, so
that you reach your goal?
0 11 2
RM1210RM1210
10%
PVPV00
Present Value (Graphic)

14. •Excel makes these calculations easy with the use of the built-inExcel makes these calculations easy with the use of the built-in
functionfunction PV:PV:
PV(Rate,Nper,PMT,FV,PV(Rate,Nper,PMT,FV,TypeType))
•There are five parameters to theThere are five parameters to the PVPV function.function.
•RateRate :: is the interest rate per period (year, month, day, etc)is the interest rate per period (year, month, day, etc)
•NperNper :: is the total number of periodsis the total number of periods
•FVFV :: is the future valueis the future value
•PMTPMT andand TypeType are included to handle annuities (a series of equalare included to handle annuities (a series of equal
payments, equally spaced over time)payments, equally spaced over time)
*f*for problem of the type that we are currently solving, we will set both PMT andor problem of the type that we are currently solving, we will set both PMT and TypeType
to 0to 0
Present Value (Microsoft Excel)

15. •The result is RM1000.
•Note we have entered –B1 for the FV parameter.
•The reason for the negative sign is that Excel realizes that
either the PV or FV must be a cash flow.
*if we had not used the negative sign, the result (PV) would have been negative.
Present Value (Microsoft Excel)

16. Jali needs to know how large of a deposit to make
today so that the money will grow to RM2,500RM2,500 in 55
years. Assume today’s deposit will grow at ayears. Assume today’s deposit will grow at a
compound rate ofcompound rate of 4% annually.
Present Value Example
0 1 2 3 4 55
RM2,500RM2,500
PVPV00
4%

17. Annuities
• Examples of Annuities Include:
- Student Loan Payments
- Car Loan Payments
- Insurance Premiums
- House Payments
An AnnuityAn Annuity represents a series of equal
payments (or receipts) occurring over a
specified number of equidistant periods.

18. •It is the lump sum payment today that would be
equivalent to the annuity payments spread over the
annuity period.
Present Value Of An Annuity
(PVA)

19. PVAPVA33 = RM1,000/(1.07)1
+ RM1,000/(1.07)2
+
RM1,000/(1.07)3
= RM2,624.322,624.32
If Ali agrees to repay a loan by paying RM1,000 aIf Ali agrees to repay a loan by paying RM1,000 a
year at the end of every year for three years and theyear at the end of every year for three years and the
discount rate is 7%, how much could one borrowdiscount rate is 7%, how much could one borrow
today?today?
Example of an Ordinary
Annuity -- PVA
RM1,000 RM1,000 RM1,000
0 1 2 33 4
RM2,624.32 = PVARM2,624.32 = PVA33
End of Year
7%
RM934.58
RM873.44
RM816.30

20. •In Excel, we are using the PV function by inserting
components below:
PV (Rate, Nper, PMT, Type)
•Rate : interest rate
•Nper : total number of payments in an annuity
•PMT : fixed payment made each period
•Type : 0 (payment at end of period), 1 (payment at
beginning of period)
PVA (Microsoft Excel)

21. •That means Ali should borrow RM2624.32 and
deposit it into an account today which pay 7% interest
per year, then he could repay its loan RM1000 at the
end of every year for three years.
PVA (Microsoft Excel)

22. •It is compound annuity that involves depositing or
investing an equal sum of money at the end of each year
for a certain number of years and allowing it to grow.
or the total amount one would have at the end of the
annuity period if each payment were invested at a given
interest rate and held to the end of the annuity period.
Future Value Of An Annuity
(FVA)

23. FVAFVA33 = 1,000(1.07)2
+ 1,000(1.07)1
+
1,000(1.07)0
= RM3,215RM3,215
If Ana saves RM1,000 a year at the end of everyIf Ana saves RM1,000 a year at the end of every
year for three years in an account earning 7%year for three years in an account earning 7%
interest, compounded annually, how much willinterest, compounded annually, how much will
one have at the end of the third year?one have at the end of the third year?
Example of an Ordinary
Annuity -- FVA
RM1,000 RM1,000
0 1 2 33 4
RM3,215 = FVARM3,215 = FVA33
End of Year
7%
RM1,070
RM1,145
RM1,000

24. •In Excel, we used the FV function by inserting
components below:
FV (Rate, Nper, PMT, Type)
•Rate : interest rate
•Nper : total number of payments in an annuity
•PMT : fixed payment made each period
•Type : 0 (payment at end of period), 1 (payment at
beginning of period)
FVA (Microsoft Excel)

25. •That means Ana will have RM3214.90 at the end of
the third year if she saves RM1000 a year at the end of
every year for three years in an account earning 7%.
FVA (Microsoft Excel)

26. Problem #1
You must decide between RM25,000 in cash today
or RM30,000 in cash to be received two years from
now. If you can earn 8% interest on your
investments, which is the better deal?
“Remember!! both quantities must be present value
amounts OR both quantities must be future value
amounts in order to be compared.”

27. PMT
• Used to calculate the payment for a loan based on
constant payments and a constant interest rate.
• It can be calculated for PV or FV of an annuity.

28. • Components involved are:
PMT ( Rate, Nper, PV/FV, Type )
Rate : interest rate
Nper : total number of payments in an annuity
PV : present value
FV : future value
Type : 0 (payment at end of period), 1 (payment
at beginning of period)
PMT

29. Example
Frank Seator wishes to determine the equal annual end
of year deposits required to accumulate RM5000 at the
end of 5 years when his son enters college. Assume
interest rate is 10 %.
PMT

30. Solving For The Number Of
Periods In An Annuity
Excel offer the built-in NPER function to solve problem of
this type. This function is defined as:
NPER (Rate, PMT ,PV, FV, Type)
How many years it will take to prepare a down payment as
much as RM10000 to buy a house later on in the future if
RM1846 per year is kept in the bank and the rate is 4% per
year?

31. Solving For The Interest In
An Annuity
Unlike the present value, future value, payment and
number of periods, there is no closed form solution for
the rate of interest of an annuity. The only way to solve
this problem is to use a trial and error approach.
Built-in function in Excel can solve the interest rate:
RATE (NPer, PMT, PV, FV, Type)

32. Example:
Suppose that you are approached with an offerSuppose that you are approached with an offer
to purchase an investment, which will provideto purchase an investment, which will provide
cash flow of RM1500 per year for 10 years. Thecash flow of RM1500 per year for 10 years. The
cost of purchasing this investment is RM10500.cost of purchasing this investment is RM10500.
if you have alternative investment opportunity,if you have alternative investment opportunity,
of equal risk, which will yield 8% per year,of equal risk, which will yield 8% per year,
which should you accept?which should you accept?

33. Lab exercise
1. To what amount will RM3000 grow if Ali invested
it at 12% compounded annually for 5 years?
2. How much Siti should pay today to receive
RM12000 in 5 years if she wants to earn 10%
interest compounded annually.
3. Jane wishes to determine the sum of money she
will have in her savings account at the end of 6
years by depositing RM1000 at the end of each
year for the next 6 years. The annual rate is 8%.
4. Calculate the PV, discounted at 10%, of receiving
RM500 a year fro the next 10 years.

34. Lab exercise
5. A company intends to sell a lorry.
- Offer A: RM60000 cash
- Offer B: 5 years instalment of RM5500 at the end
of each year.
- Offer C: RM10000 cash, 5 years instalment of
RM1000 at the end of each year with another
cash payment of RM10000 at the end of fifth
year.
Which is the best offer? Let the interest rate be 10%
per year.

35. Lab exercise
6. You currently have RM25000 and can afford to
invest RM5000 every year. You would like to be a
millionaire in 25 years’ time. What interest rate
would be needed to achieve the goal?
7. Azlan needs to borrow RM250000. The rate of
the loan is 2% and he can afford payments of
RM13000 a year. How long will it take to repay
the loan?