Summary FBS 210 - Chapter 2 Time Value of Money

LA 4 – TIME VALUE OF MONEY
 Time value of money allows the comparison of cash flows from different time periods
 It is a basic financial concept that holds that money in the present is worth more than the same sum of
money in the future (money you have now can be invested and you can earn a return/interest)

PRESENT VALUE PV  The value of the investment in the beginning, it is your starting amount
 Sometimes referred to as the principle sum
 (-)
FUTURE VALUE FV  The amount of cash that will have grown from the initial amount
 Always bigger than your PV as long as it is earning interest and growing over
time
 (+)
NUMBER OF N  The number of periods
PERIODS
INTEREST RATE I/YR  Growth rate over your money over a certain period of time
PER PERIOD
PAYMENT PMT  Periodic investments/installments made
AMOUNT  Can be at the beginning/end of each period
NUMBER OF P/YR  When interest is compounded more than once in a year
PAYMENTS PER  NB: this should always be 1 in your calculator
YEAR

(+) inflow of money
(-) outflow of money




COMPOUND INTEREST

 This is always better to use over simple interest because you get a bigger FV because you earn interest on
interest
 interest can be compounded more than once in a year

Yearly/Annually Compounded once a year Type everything normally on your
calculator
Half-yearly Compounded 2 times a year N=x2
I/YR = / 2
Quarterly Compounded 4 times a year N=x4
I/YR = / 4
Monthly Compounded 12 times a year N = x 12
I/YR = / 12
Daily Compounded 365 times a year N = x 365
I/YR = / 365
Continuously Compounded an infinite number of Eg:
times a year You invest R100 with an interest rate of
12% compounded continuously

Calc:
0.12 – INPUT – SHIFT – e x – x – 100 – =

, NOMINAL AND EFFECTIVE INTEREST RATES

It is useful to be able to convert a nominal interest rate into an effective interest rate for many reasons, particularly
in order to compare investment alternatives with different compounding periods

Example

Interest rates on investments accounts quoted by 3 banks
 Bank A: 15% compounded daily
 Bank B: 15.5% compounded quarterly
 Bank C: 16% compounded annually

Which bank should you borrow from?

BANK A BANK B BANK C
1. Change the P/YR to 365 1. Change the P/YR to 4 1. Change the P/YR to 1
2. 15 – SHIFT – NOM% - SHIFT 2. 15.5 – SHIFT – NOM% - SHIFT – EFF% 2. 16 – SHIFT – NOM% - SHIFT –
– EFF% EFF%
EFF% = 16.18% EFF% = 16.42% EFF% = 16%

Therefore, Bank B would be best bank to borrow from as they offer the highest interest rate

NOTE (1):
 If your interest is compounded annually, your nominal and effective interest rate will be the same
 NB – make sure you change your P/YR back to 1 before continuing with other questions

NOTE(2):
If interest is compounded monthly but payments are made ANNUALY, you must change your nominal interest rate
into an effective interest rate before you do your calculation. This is because your calculator assumes that PMT and
I/YR occur at the same frequency


ANNUITIES

 Annuities are equally spaced cash flows of equal size
 They can either be inflows or outflows
 Cash flows on calculator – use PMT function

ORDINARY ANNUITY Cash flow at the end of the year
ANNUITIY DUE Cash flow at the beginning of the year
NB – use BEG mode on calculator

Example

Calculate the FV of an ordinary annuity if you deposit Calculate the FV of an annuity due if you deposit R100
R100 at the end of each year for 3 years at an interest at the beginning of each year for 3 years at an interest
rate of 12% compounded annually. rate of 12% compounded annually.

PMT = -100 *make sure your calculator is in BEG mode (SHIFT –
N = 3 years MAR)
I/YR = 12%
PMT = -100
FV= R337.44 N = 3 years
I/YR = 12%

FV= R337.93