TIME VALUE OF
MONEY
BSA - 3
BERNABE, AR-JAY D.
DAKIS, LEONARD D.
What is Time
Value of Money
The time value of money (TVM)
is the concept that a sum of money is
worth more now than the same sum will be
at a future date due to its earnings
potential in the interim.
is a core principle of finance.
Why is the Time
Value of Money
Important?
Why is the Time Value of Money Important?
A dollar today is worth more than a dollar
tomorrow.
Question : would you rather have $1,000
today or $1,000 in five years?
Why is the Time Value of Money Important?
Inflation erodes the purchasing power of
money over time, decreasing its future
value.
Understanding the TVM allows us to
compare the value of money at different
points in time and make informed financial
decisions.
Key Factors
Affecting the Time
Value of Money
Key Factors Affecting the Time Value of
Money
Present Value (PV): The current worth of a
future sum of money, discounted at a
specific interest rate.
Future Value (FV): The value of a current
sum of money in the future, grown at a
specific interest rate over a specific time
period.
Key Factors Affecting the Time Value of
Money
Interest Rate (r): The cost of borrowing
money or the return on an investment,
expressed as a percentage.
Time (t): The duration for which the money
is invested or borrowed, usually expressed
in years.
Formulas for
Calculating the
Time Value of
Money
Present Value (PV)
Formula:
PV = FV / (1 + r)^n
PV = Present Value
r = Interest Rate per period
n = Number of periods
For example, the present-day peso amount
compounded annually at 7% interest that would
be worth P5,000 one year from today is:
Formula:
PV = FV / (1 + r)^n PV = [5,000] / 1+7% ^ 1
PV = P5,000 = P4,673
r = 7%
n = 1 year
Let's say you inherit P10,000 in five years.
You expect to earn an annual interest rate of 8% on
your investments.
What is the Present Value of that P10,000 inheritance?
Formula:
PV = P10,000 / (1 + 0.08)^5
PV = FV / (1 + r)^n
PV ≈ P6,805.19
PV = P10,000
r = 8%
n = 5 years
Future Value (FV)
Formula:
FV = PV * (1 + r)^n
PV = Present Value
r = Interest Rate per period
n = Number of periods
Let's assume a sum of P10,000 is invested for one
year at 10% interest compounded annually. The future
value of that money is:
Formula:
FV = PV * (1 + r)^n PV = P10,000 * (1 + 10%)^1
PV = P10,000 PV ≈ P11,000
r = 10%
n = 1 year
Effect of Compounding Periods on Future Value
The number of compounding periods has a dramatic effect
on the TVM calculations. Taking the 10,000 examples
above, if the number of compounding periods is increased
to quarterly, monthly, or daily, the ending future value
calculations are:
Quarterly
Compounding:
Why is the Time Value of Money Important?
Inflation erodes the purchasing power of
money over time, decreasing its future
value.
Understanding the TVM allows us to
compare the value of money at different
points in time and make informed financial
decisions.
Simple vs.
Compounded
Effective Interest
Simple Interest
A straightforward method for calculating
interest earned on an investment or loan.
Considers only the initial principal
amount for the entire investment period.
Interest is calculated as a flat rate applied
to the principal amount for the time
period.
Simple Interest
Formula:
= Pxrxn
where:
P = Principal amount
r = Annual interest rate
n = Term of loan in years
Example: Calculating Simple Interest Earned
Let's say you borrow $1,000 from a friend for one year
to fix your car. You agree to repay the loan with a
simple interest rate of 5%.
Identify the variables:
Principal (P) = $1,000 I = (P1,000) x (5%) x (1 year)
Interest Rate (R) = 5%
Time (T) = 1 year I = P50
Compound Interest
Interest is earned on both the initial
principal amount and the accumulated
interest from previous periods.
Often referred to as "interest on interest."
Leads to a more significant growth in
investment value over time due to this
snowball effect
Formula for Compounded Interest
FV = P(1 + r)^n
Where:
FV = Future Value
P = Principal Amount
r = Interest Rate (per period)
n = Number of Compounding Periods
Example: Growing your Savings with Compounding
Interest
Imagine you decide to be proactive with your finances
and start saving for a down payment on a house. You
deposit P5,000 into a savings account that offers a
3% annual interest rate compounded monthly
(meaning interest is calculated and added to your
balance every month). You plan to save for 5 years.
Identify the variables:
Principal (P) = P5,000 (initial deposit)
Interest Rate (R) = 3% per year (divided by 12 for
monthly compounding: 0.25% per month)
Number of Compounding Periods (n) = 5 years x 12
months/year = 60 months
FV = P(1 + r)^n
FV = P5,000 (1 + 0.0025)^60
FV = 6,473.14
Present Value of
an Ordinary
Annuity Example
The present value formula for an ordinary annuity
takes into account three variables. They are as
follows:
PMT = the period cash payment
r = the interest rate per period
n = the total number of periods
Given these variables, the present value of an
ordinary annuity is:
Present Value = PMT x ((1 - (1 + r) ^ -n ) / r)
For example, if an ordinary annuity pays P50,000
per year for five years and the interest rate is 7%,
the present value would be:
PMT = P50,000
r = 7%
n = 5 Years
Present Value = P50,000 x ((1 - (1 + 0.07) ^ -5) / 0.07)
= P205,010
If the annuity in the above example was instead
an annuity due, its present value would be
calculated as:
Present Value of Annuity Due =
P50,000 + P50,000 x ((1 - (1 + 0.07) ^ -(5-1) / 0.07)
= P219,360
THANK YOU
FOR YOUR ATTENTION
1. ________ is a core principle of finance.
2. ________ is the current worth of a future sum of
money, discounted at a specific interest rate.
3. __________The cost of borrowing money or the
return on an investment, expressed as a
percentage.
4. _________ The duration for which the money is
invested or borrowed, usually expressed in
years.
5. _______ A straightforward method for calculating
interest earned on an investment or loan.
6. _______ Often referred to as "interest on
interest."
7. Scenario:
You invest $2,000 into a certificate of deposit (CD)
with a term of 2 years. The CD offers a simple
interest rate of 4% per year.
Question:
What will be the total amount of interest earned on
the investment after 2 years?
8 and 9 : Let's say you have $10,000 to invest and are considering
two different options:
Option 1: Invest in a savings account with an annual interest rate
of 2% compounded annually. You plan to invest for 7 years.
Option 2: Invest in a mutual fund with an annual interest rate of 8%
compounded monthly. You plan to invest for the same 7 years.
Challenge:
Calculate the future value of your investment for each option after
7 years.
Determine which option offers a higher return on your investment
due to compounding.
10. You are considering joining a gym membership that
offers a monthly membership fee of $50 for the next two
years (24 months). You would prefer to pay the entire cost
upfront to receive a discount. The gym offers a 10%
annual discount rate (divided by 12 for monthly
compounding: 0.833% per month).
Question:
What is the present value (discounted price) you would
need to pay upfront to cover the entire 2-year
membership?
ANSWERS:
1. TIME VALUE OF MONEY
2. PRESENT VALUE
3. INTEREST RATE
4. TIME
5. SIMPLE INTEREST
6. COMPOUND INTEREST
ANSWERS:
7.Solution:
Identify the variables:
Principal (P) = $2,000 (initial investment)
Interest Rate (R) = 4% per year
Time (T) = 2 years
Use the simple interest formula:
I = PRT
I = ($2,000) x (4%) x (2 years)
I = $160.00
Option 1: Savings Account (Compounded Annually)
Identify the variables:
Principal (P) = $10,000
Interest Rate (R) = 2% per year
Number of Compounding Periods (n) = 7 years
Use the compound interest formula:
FV = P(1 + r)^n
FV = $10,000 (1 + 0.02)^7
Calculate the Future Value (approximately):
FV ≈ $11,487.20
Option 2: Mutual Fund (Compounded Monthly)
Identify the variables:
Principal (P) = $10,000
Interest Rate (R) = 8% per year (divided by 12 for monthly
compounding: 0.67% per month)
Number of Compounding Periods (n) = 7 years x 12
months/year = 84 months
Use the compound interest formula:
FV = P(1 + r)^n
FV = $10,000 (1 + 0.0067)^84
FV ≈ $21,911.23
Solution:
Identify the variables:
P (PMT) = $50 (monthly membership fee)
(n) = 2 years x 12 months/year = 24 months
(r) = 10% per year / 12 months/year = 0.833% per month
Use the present value formula for an ordinary annuity:
PV = PMT x [ 1 - (1 + r)^(-n) ] / r
PV = $50 x [ 1 - (1 + 0.00833)^(-24) ] / 0.00833
Calculate the Present Value (approximately):
PV = $1,074.59.
