TIME VALUE OF MONEY USING IN FINANCIAL

MARKET

Concept of Time Value of Money 1. Classical theory:

 Time value of money denotes the value of money  Oldest theories concerning the determination of
over time. This means that money changes its value the pure or risk- free interest rate developed
over time. P1 today no longer be P1 after a year. during the eighteenth and nineteenth centuries by
 Time value of money is central to the concept of a number of British economists, refined an
finance. Australian economist Bohm- Bawerk, and
elaborated by Irving Fisher early in the 20th
Inflation is an economic disorder characterized by
century.
continuous increase in the price level of goods and
services without the corresponding increase in the  This theory posits that the rate of interest is
production of these goods and services. determined by two factors:
The concept of the value of money is based on the 1. Supply of saving
notion that the peso received today is worth more than a
2. Demand for capital investment.
peso received in the future.

INTEREST RATES AND THEIR ROLE IN FINANCE  Saving generally carried on by individuals and
families (households) and for these households,
 Interest rate denotes percentage earning or yield
they are simply abstinence from consumption
on investment
spending.
 It is the cost of using money expressed as a  Consumption spending means spending for both
percentage of the principle for a given period of durable and non- durable goods and services.
time, which is usually per year.
2. Loan Funds Theory
TYPES OF INTEREST  Used for forecasting interest rate.
1.Real Interest Rate  This theory is based on the premise that the
interest rate is the price paid for the right to
 Named because it states the “real” rate that the borrow or use loanable funds.
lender or investor receives, or a borrower pays after
considering inflation. 3. Liquidity Preference Theory

 Interest rate that is adjusted for expected changes  In 1930, John Maynard Keynes introduced the
in the price level to accurately reflect the true cost concept of money demand and used the term
of borrowing. “Liquidity preference” for demand.

2.Fixed Interest Rate  This theory stipulates that the interest rate is
determined in the money market by the money
 Interest rate that you will be charged over the term
demand and money supply.
of your loan will not change, no matter how high or
low the market may drive the interest rate.  Interest rate is the point where the money
demand is equal to the money supply.
3. Variable Interest Rate
4. Rational Expectation Theory
 Also called floating rate
 Theory came out in the advent of the information
 Interest you are charged changes as whatever age.
index your loans are based on changes.
 Based on the precise that the financial markets
 The index can be the rate on T-bills, the prime are highly efficient institutions in digesting new
lending rates of banks, or the LIBOR. information affecting interest rate and security
prices.

Interest rate theories DETERMINANTS OF INTEREST RATE

  Inflation expectation j m
U = (1+ ¿ -1
 Monetary policy
m

 Business cycle 1. What is the effective rate that is equivalent to 9 %

compounded semi-annually?
 Government budget deficits 2. What is the nominal rate compounded quarterly is
equivalent to 6 % effective rate?
SIMPLE AND COMPOUND INTEREST
VARYING INTEREST RATE
Interest, in financial parlance, is the money paid for the
use of money lent. Interest is measured by a certain  When the interest rate of an investment changes
percentage commonly known as interest rate. With during its term, then it is called investment with a
interest, the value of money after some period of time varying interest rate.
grows.
1. How much will be the compound amount of P
Two basic types of interest measurement
30,000.00 at the end of 15 years if it is invested at
 Simple interest 8% compounded semi annually in the first 5 years,
 Compound interest 7 % compounded quarterly in the next 5 years, and
6 % compounded monthly in the remaining years.
SIMPLE INTEREST 2. P 50,000.00 is invested for 20 Years that pays 6%
compounded quarterly for the first 5 years, 7 %
I =P x R x T
compounded semi – annually for the next 5 years
 P= PRINCIPAL and 8% compounded annually for the next 10
 R= INTEREST RATE years. How much will be the maturity value at the
 T= TIME PERIOD MONEY IS BORROWED/ end of 20 years.
INVESTED
CONTINUOUS COMPOUNDING OF INTEREST
EXAMPLE:
 Interest on investment may also be compounded
1. A man borrowed P 25,000 for 2 ¼ year at 8% frequently such as daily, or weekly. In such cases,
per year. Find the amount of simple interest. the frequent conversion will increase the interest
2. Find the amount of simple interest on a loan of P slightly only. This method of compounding very
13,400.00 for 1 2/3 years at 8 ¾ %. frequently is called continuous compounding of
3. How much is simple interest on P 17,600 for 7 interest.
months at 7.5%. jt
4. A loan of P 28,900.00 is obtained for 5 months at M =Pe
8 3/5 percent. How much is the simple interest. WHERE: e is a constant of which value is
5. A man obtained loan of P 54,000.00 for 2 year approximately 2.71828
and 11 months at 8.35%. How much was the
simple interest. EXAMPLE:

EXACT AND ORDINARY INTEREST 1. How much will be the maturity value of P
20,000.00 at the end of 5 years if the interest rate
6. An amount of P 37,500 was borrowed at 8 ½ is 8% compounded continuously?
percent simple interest 120 days. 2. If an investment accumulated to P 50,000.00 at
NOMINAL AND EFFECTIVES RATE the end of 5 years when the interest rate 7 %
compounded continuously, how much was the
 A nominal rate is rate of interest that is original amount.
compounded more often than once a year such as
semi annually, quarterly or monthly.
 An effective rate is that the rate when
compounded annually produces the same
compound amount each year as the nominal rate (j)
compounded (m) times a year.
MATURITY VALUE
J = m ¿ ¿ - 1]
  When a certain amount of money is deposited or 7. P 25, 750.25 for 3 year and 5 months at 8 ¼ %
borrowed, the sum of money at the end of the compounded monthly.
period is called maturity or accumulated value.
PRESENT VALUE ON COMPOUND INTEREST
M =P ( 1+ RT )∨ M =P+ PRT −n
P=M (1+i)
EXAMPLE:
Find the present value of:
1. Find the maturity value of a loan of P 18,000 made
for 2 years at 8 % at simple interest. 1. P 12,850.00 due in 3 years if the interest rate is
2. A sum of P 43,200 is borrowed for 11 months at 7 8% Compounded quarterly
1/5 percent simple interest. Determine the maturity 2. P 49,250.45 due in 5 years and 5 months if the
of the loan. money is worth 6 2/5 percent compounded
COMPOUND INTEREST monthly.

 Compound interest is calculated on the original PRESENT VALUE AND DISCOUNTING

principal and the interest previously earned by an  The present value is the value at the current time
account. This means that a sum of money of the cash flow expected to the received after
invested for one year that earns interest some period of time. It answers the question of
compounded quarterly will earn simple interest for how much is the worth today of an amount that will
the first quarter. be received in the future. The method of
 Compound interest is usually used by banks in determining the present value is called
calculating interest for the long-term investment discounting.
and loan such as saving accounts and time
deposits PV =CF ¿ ¿]
J n 1. The investor received a cash flow of P 1,000,000
M=P (1+ ¿ ∨¿ M =P ¿
m after 5 years with a discount rate of 5%.

 P = Original Principal COMPOUND INTEREST (RATE UNKNOWN)

 M= Compound amount or maturity value or 1
accumulated value of P at the end of n periods M n -1] x 100 %
J = m [( ¿¿
 J = nominal rate or annual rate of interest P
 M = frequency (f) of conversion period
 At what rate of interest compounded annually will
 I = interest rate per conversion period
P 60,000.00 accumulate to P 70,000.00 in 2 years.
 T = term of investment or loan a year
 N = total number of conversion period of COMPOUND INTEREST (TIME UNKNOWN)
investment term
M
EXAMPLE: log
t (in years) = P ) +m
Find the compound amount and compound interest. log ⁡(1+i)
1. P 10,000 for 5 years at 6% compounded annually  How many years will it take for P13,000.00 to
become P 20,000 if is invested at 8% compounded
2. P 15, 250.00 for 4 years and 6 months at 8%
quarterly.
compounded semi annually
ANNUITY
3. P 20,250.00 for 5 years and 9 months at 9%
compounded quarterly  An annuity is defined as a stream or series of
payment made or receipt received over time.
4. P 25, 750.25 for 3 year and 5 months at 8 ¼ %
 Annuity problems involve a series of equal
compounded monthly.
periodic payments or receipt called rents.
5. P 10,000 for 5 years at 6% compounded annually

6. P 15, 250.00 for 4 years and 6 months at 8%  An Ordinary Annuity is an annuity in which the
compounded semi annually payments are made at the end of each payment
interval.
  An Annuity Due is an annuity in which the FV = P(1+r )n
payments are made at the beginning of each
payment interval. Problem 1: Future value of annuity

 A Deferred Annuity is an ordinary annuity in What is the future value (as of 10 years from now) of an
which the first payment is made at some later annuity that makes 10 annual payments of 5,000, if the
date. interest rate is 7% per year compounded quarterly?

PRESENT VALUE OF AN ORDINARY ANNUITY ( A0 ) Problem 2: Future value of annuity due

 The present value of annuity is the sum of money An annuity makes 25 annual payments of 1,000 with the
today which if invested at specified rate will first payment coming today. What is the future value of
amount to all payment and compound interest at this as of 25 years from now if the interest rate is 9%?
the end of the term of the annuity.

A0 =R ¿]

A0 = present value of ordinary annuity

R = Amount of payment period

I = rate of interest per conversion period

N = number of payments periods

EXAMPLE:

1. Find the present value of an ordinary annuity

whose periodic payment of P 15,000.00 is payable
at the end of each 6 months for 10 years at 8%
compounded semi-annually.

2. Mr. Romero wants to deposit a sum of money that

will give an ordinary annuity paying P 12,000.00
quarterly for the next 6 years, if the interest is
8.8% compounded quarterly and withdrawals will
be made at the end each quarter. Find the present
value of ordinary annuity.

3. Find the present value of an annuity due whose

periodic payment of P 12,000.00 is payable per
quarter at 8% compounded quarterly for 5 years.

FUTURE VALUE AND COMPOUNDING

 Future value is the sum of money which will be

received in the future resulting from investment,
taking into account the interest it will earn. It is
synonymous with the terms “terminal value” and
maturity value. Compounding or accumulation is
the process in which future value is determined.

Assuming P 1,000,000 is invested in a 4- year, 10 %

financial assets.