3. Identifying the a) principal, b) interest rate, and
time period in the examples below.
1. Your mother invested P 18 000 in government securities that
yields 6% annually for two years.
2. Your sister placed her graduation gifts amounting to P 25 000 in a
special savings account that provides an interest of 2% for 8
months.
3. Your brother borrowed from your neighbor P 7 000 to buy a new
mobile phone. The neighbor charged 11% for the borrowed
amount payable after three years.
4. You deposited P 5 000 from the savings of your daily allowance in
a time deposit account with your savings bank at a rate of 15% per
annum. This will mature in 6 months.
4. Interest
• In general business terms, interest is defined as
the cost of using money over time. This
definition is in close agreement with the
definition used by economists, who prefer to say
that interest represents the time value of money.
• is the excess of resources (usually cash) received
or paid over the amount of resources loaned or
borrowed which is called the principal
5. SIMPLE INTEREST
• is the product of the principal amount multiplied
by the period’s interest rate (a one-year rate in
standard).
𝐈 = 𝐏 × 𝐑 × 𝐓
where:
I = interest
P = Principal
R = Interest rate
T = Time period
6. Example 1:
You invested P 10 000 for 3 years at 9% and the
proceeds from the investment will be collected at
the end of 3 years. Using a simple interest
assumption, the calculation will be as follows:
7. COMPOUND INTEREST
• is the interest paid on both the principal and the amount of
interest accumulated in prior periods.
FV= 𝑷(𝟏 + 𝒊)𝒏
• where:
FV = Future Value
P = Principal
i = Interest rate per compound interest period or
periodic rate
n = Time period or number of compound
interest periods
Subtract the principal from the future value to get the
compound interest. Hence, Ic= FV – P.
8. • Example 2: Using example 1 where you invested
P 10 000 for 3 years at 9% and the proceeds
from the investment will be collected at the end
of 3 years, compound interest will be computed
as follows:
9. FUTURE VALUE OF MONEY
• is the value of the present value after n time
periods.
• To account for time value for single lump-sum
payment, we use the same formula provided for
under compound interest rates
FV= 𝑷𝑽(𝟏 + 𝒊)𝒏
where, PV = Present Value
(𝟏 + 𝒊)𝒏 = Future value interest factor
(FVIF)*
10. • Example 3: Using the formula, find the future
values of P 1 000 compounded at a 10% annual
interest at the end of one year, two years and five
years.
11. • Example 4: Determine the compound amount
on an investment at the end of 2 years if P 20
000 is deposited at 4% compounded a) semi-
annually and b) quarterly.
12. PRESENT VALUE OF MONEY
• To get the present value of a lump-sum amount,
PV= 𝑭𝑽(𝟏 + 𝒊)𝒏
• where, (𝟏 + 𝒊)𝒏 = Present value interest factor
(PVIF)* or discount factor
13. 1. Lisa receives an amount of P 20 000 deposited in her account on
her 18th birthday. If the bank pays 6% interest monthly and no
withdrawals are made, how much should be credited in her
account on his 21 st birthday?
2. James borrows P 5 000 with interest at 15% quarterly. How much
should he pay at the end of 2 years and 6 months to settle her
debt?
3. Mr. Santos invested P 15 000 in an account for each of his
children. The accounts paid 8% compounded semi-annually.
Determine the balance of each account for the following:
a. The youngest child withdrew the balance after 5 years for
college
b. The second child withdrew the balance after 8 years to buy a
car
c. The third child withdrew the balance after 10 years to travel
4. A man wishes to accumulate P 10 000 in 2 years, how much
should he invest now at 15% compounded semi-annually?
5. What is the present worth of P 5 000 for 2 years at 12%
compounded quarterly?
EVALUATION
14.
15. ANNUITIES
• An installment that requires a buyer to pay equal
payments at a certain period illustrates an
annuity – a series of equal cash flow – payments
in this case for a specific number of periods.
• If payment is made and interest is computed at
the end of each payment interval, then it is
called ordinary annuity.
16. • To get the present value interest factor for an
ordinary annuity (FVIFA) use the formula
below:
•
• Where, R = regular payment
• To get the future value of an ordinary annuity,
use this formula:
17. • Example 6:
• What lump sum would have to be invested at 6%
compounded annually to provide an ordinary
annuity of P 10 000 per year for 4 years?
18. • If the cash flow happens at the beginning of each
period, then it is called a annuity due. The
formulas to use are shown below:
19. • Example 7: If a supplier would allow you to pay
P 50 000 annually at 10% for 3 years with the
first payment due immediately, how much would
be the present value and the future value?
20. • If the cash flow stream lasts forever or is
indefinite, then it is called a perpetuity. The
formula for present value of a perpetuity is
simply
21. LOAN AMORTIZATION
• refers to the amount of principal and interest
paid each month over the course of your loan
term.
• For some corporate long-term loans, principal
payment is fixed, and the interest expense is
adjusted based on the declining principal
balance.
22. • Example 8: On July 1, 2015, DD Company borrowed P 3 million
from ASC Bank at the rate of 10% a year. The loan is paid at the rate
of P 500 000 every December 31 and June 30 until the full amount
is paid. Below is an amortization table for the loan.
23. • To compute for the interest expense from June
30 to December 31, 2015:
Interest = 3 000 000 x 10% x (6 /12)
= 150 000
• To compute for the equal regular payment, use
the formula in annuity
24. • Example 9: You borrowed P 50 000 from a bank to buy a
mobile phone. Assuming you need to repay the loan by
equal payments at the end of every 6 months for 3 years
at 10% interest compounded semi-annually. What is
your periodic payment?
25. NET PRESENT VALUE METHOD
• to determine whether a project should be
accepted or rejected by a company.
• The basic decision rule is to accept the project if
the net present value is positive and reject if it is
negative.
• The basic formula is:
NPV = PV of Inflows – PV of Outflows
or
NPV = PV of Future Cash Flows – Initial Investment
26. • Example 10: A company wants to purchase an
equipment that will cost P 100 000 and estimated to be
used for 5 years. Operating cash inflows from the use of
equipment would be P 50 000 while annual operating
cash outflows (due to repairs and maintenance) are
estimated at P 10 000. Compute for the NPV.
27. RISK-RETURN TRADE-OFF
• In finance, we assume that individuals are risk
averse but have different levels of risk aversion.
• Risk aversion means that individuals
maximize returns for a given level of risk or
minimize risk if the returns are the same. Risk-
averse individuals would require a higher return
if the risk level increases.
28. • In general, the riskier the investment, the higher
the potential return should be, indicating a direct
relationship between risk and potential return. As
a business owner you should know to balance the
risk and the potential return of your investments.
• Risk is defined here as the uncertainty of returns.
One way to reduce risk to an acceptable level is
through diversification wherein you invest in
different types of investments with different risks
and returns. This is an application of the saying:
• “ Don’t put all your eggs in one basket.”
