SIMPLE INTEREST Example 1

Suppose you put PhP280, 000 in a bank at

Simple interest 0.75% simple interest rate. If you leave this
● characterized by a fixed amount amount in a year in a bank, how much
earned over time money will you have in your account at the
For example, if you saved Php 100, 000 at end of the year?
2% simple interest, you will earn Solution:
P = 280, 000,
(100, 000)(0.02) = Php 2, 000, after a year. r = 0.75% = 0.0075,
Your initial money of Php 100, 000 will be t=1
Php 102, 000 after a year. F=?
F = P (1 + rt)
*Php 100, 000 is called the present value
*Php 102, 000 is called the future value F = 280, 000(1 + 0.0075(1))
= 280, 000(1.0075)
Present value = 282, 100
● the current value of a sum of money
or assets given a specified interest Example 2
rate Find the interest earned after 3 years if Php
Future value 12, 000 is deposited in a savings account
● the value of current money or assets that earns 5% simple interest.
at a specified date in the future Solution:
based on the given interest rate. t = 3,
P = 12, 000,
Simple interest Formula: r = 5% = 0.05.
I = Prt I =?
I = Prt
P = Principal Amount
R = Rate of Interest = (12, 000)(0.05)(3)
t = time in years = 1, 800
I = Interest earned *After 3 years, the interest earned is
Php 1, 800
The amount after t years is denoted by F
and the formula is given by: Example 3
F = P (1 + rt), How long will it take a Php 30, 000 debt to
earn an interest of Php 4, 500 if the simple
P = principal amount interest being charged is 9%?
r = rate of interest per year Solution:
t = time in years P = 30, 000
I = interest I = 4, 500
F = Future Value r = 9% = 0.09
t=?

Solving for t from I = P rt, we have

 𝐼 COMPOUND INTEREST
t= 𝑃𝑟
4. 500
= *you will earn money not only on what you
(30, 000)(0.09)
have saved but also on the interest you
= 1.67
received on that money.
Convert to days: (1.67)(365) = 245 days.
𝑟 𝑡𝑚
F=P(1+ 𝑚
)
*This means that in 1.67 years or 1 year
and 245 days, interest of Php 4, 500 will be P = principal
earned for a Php 30,000 debt with an r = rate of interest per; annum or per year
interest rate of 9% t = time in years,
m = number of times interest is computed
Example 4 per year
How much is the maturity value if Php 14,
500 is placed in a account earning 6.25%
If interest is compounded:
simple interest for 18 months?
Solution: yearly: m = 1 Monthly: m = 12
P = 14, 500
r = 6.25% = 0.0625 Semi-annually: m = 2 Weekly: m = 52
t = 18 months = 1.5 years
F=? Quarterly: m = 4 daily: m = 365
F = P + I = P (1 + rt)
= 14, 500(1 + (0.0625)(1.5)) Example 6
= 15, 859.38 Suppose you put into your bank an amount
*The maturity value is PhP15, 859.38. of PhP280, 000. If you do not touch it for a
year and the interest is computed or
Example 5 compounded daily at 0.75%, how much is
Find the maturity value if Php 25, 000 is the maturity value of your money?
invested from October 15, 2016, to Solution:
December 15, 2017, at a simple interest P = 280, 000,
rate of 14%. t = 1 year,
Solution: r = 0.75% = 0.0075.
14 7
t = 14 months = 12
years = 6
years F=?
P = 25, 000, interest is compounded daily; thus, m = 365.
𝑟 𝑡𝑚
r = 14% = 0.14. F=P(1+ )
𝑚
F=?
F = P + I = P (1 + rt) 0.0075 (1) (365)
7 = 280, 000 ( 1 + )
= 25, 000(1 + (0.14)( )) 6
365
= 282, 107.87
= 29, 083.33
STOCKS, BONDS, AND MUTUAL FUNDS 2 Preferred stock
● entitles holders to a fixed dividend
Stocks before any payment is distributed to
● Represents shares of ownership in a other shareholders.
company ● Holders of preferred stock, in most
cases, cannot vote. In the event of
Share bankruptcy and liquidation,
● A unit of ownership of a shareholders of preferred stocks are
corporation's profits and assets paid off after creditors and before
common shareholders
Ownership
● Can be quantified by dividing the Earnings
number of shares owned by the ● per share is the amount of profit to
number of shares issued which each share is entitled.

*A stockholder receives a certificate which Market cap

contains details like the corporation’s name, ● short for Market capitalization; the
owner’s name, number of shares owned, amount of money one has to pay if
certificate number, and par value.
one buys every share of stock in a
company; calculated by multiplying
*A dividend on a share is a payment made by
the corporation to the shareholder when the the number of shares by the price
former realizes profit or has a surplus. It is per share
based on par, not on market value
IPO
Types of Stock: ● short for initial public offering occurs
1 Common stock when a company sells stocks in itself
● represents a share of the company’s for the first time Going public is a
assets and profit. Holders of slang used when a company is
common stock can vote in the planning an IPO.
election of the board of directors
(normally one vote per share). Underwriter
● The board of directors oversees the ● the financial institution or investment
management of the company but bank that does all of the paperwork
does not directly run the company. and orchestrates a company’s IPO
● Common stock is subject to high risk
and high return. Although common A stockholder can make money from stock
stocks yield a higher return than in two ways:
other stocks, common shareholders ● when earnings are paid out in the
lose the most when a company goes form of dividends
bankrupt. ● when there is an increase in share
price
The total stock return on investment (ROI) is
the sum of appreciation in the price and
dividends paid divided by the original price Solution:
of the stock, i.e Dividend yield =
𝐴𝑛𝑛𝑢𝑎𝑙 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑠𝑡𝑜𝑐𝑘 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒
11
𝑎𝑝𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝑝𝑟𝑖𝑐𝑒 = 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 Dividend yield =
Total stock ROI = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑠𝑡𝑜𝑐𝑘 𝑝𝑟𝑖𝑐𝑒
120
Dividend yield = 9.2%
Example 1
Example 3
Suppose you own shares of a company
Jen earns Php 720, 000 and can place 1/3
which just paid you Php 20 per share in
of this in savings. If she uses 50% of her
annual dividends. If the original price per
savings to buy some stocks every year, how
share is Php 1, 000 and the current price
much will she be investing annually in
per share is Php 1, 020, find the total stock
stocks?
ROI.
Solution:
Solution:
𝑎𝑝𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝑝𝑟𝑖𝑐𝑒 + 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠
● Jen’s earnings = Php 720, 000
Total stock ROI = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑠𝑡𝑜𝑐𝑘 𝑝𝑟𝑖𝑐𝑒 ● Jen’s annual savings = (720,
000)(1/3) = Php 240, 000
Total stock ROI =
(1020 − 1000) + 20 ● Jen uses 50% of her savings to buy
1000
stocks = (240,000)(0.50) = PhP120,
Total stock ROI = 4%
000
Jen will be investing PhP120, 000 annually
in stocks
Dividend per share
● the yearly dividend payment per
share
LOANS AND LOAN REPAYMENT
ONE-TIME PAYMENT
Dividend yield
Loan
● the percentage return on the
● a debt provided by one entity (an
dividend
individual or an organization) to
𝐴𝑛𝑛𝑢𝑎𝑙 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒
another entity at an interest rate.
Dividend yield = 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑠𝑡𝑜𝑐𝑘 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 ● can be repaid through a one-time or
several regular payments.
● the percentage of a stock price you
earn from a dividend.

Example 2
Suppose you own 500 shares of a certain
company, which pays PhP11 per share in
annual dividends. If the current stock price
is PhP120, find the dividend yield on the
company’s stock.
Example 1 Cash price equals down payment plus
What is the maturity value of an PhP8, 000 present value P of the balance.
3
debt payable in 2 years at 12 4
% simple
The balance is an annuity with the present
interest?
value of P given by:
Solution:
*Recall that in simple interest, the maturity value
𝑟 −𝑡𝑚
is obtained using the formula: 1 − (1 + )
F = P (1 + rt), P=R ( 𝑟
𝑚
)
P = 8, 000 𝑚
t = 2 years R = amount of the periodic payment
3
r = 12 4
% = 0.1275 r = rate of interest
m = number of payments per year
F = 8, 000 [1 + (0.1275)(2)] t = time in years
F = Php 10, 040
Example 3
Example 2 A smartphone is purchased with a
James borrows PhP700, 000 and promises downpayment of Php 1, 000 and the
to pay the principal and interest at 15% balance will be paid at Php 1, 075.83 per
compounded monthly. How much must he month for 1 year. What is its cash price if
repay after 7 years? the interest rate is 6% compounded
Solution: monthly?
𝑟 𝑡𝑚 Solution:
F=P(1+ 𝑚
) 𝑟 −𝑡𝑚
1 − (1 + )
P=R(
𝑚
P = 700, 000 𝑟 )
t = 7 years 𝑚

r = 15% = 0.15 R = 1, 075.83

m = 12 (monthly compounding) m = 12
t=1
F = 700,000 ( 1 +
0.15 (7) (12)
) r = 0.06
12
F = Php 1,987, 379.10 0.06 −(1) (12)
1 − (1 + )
= 1,075.83 (
12
0.06 )
12
−12
1 − (1 + 1.005)
SEVERAL REGULAR PAYMENTS = 1,075.83 ( )
0.005
= Php 12,500
Annuity
● is a sequence of equal payments Cash price = 1,000 + 12,500 = 13,500
made
● regularly (or periodically). The
amount of each payment is referred
to as the regular or periodic
payment, denoted by R.
Amortization
● is a debt repayment scheme in
which the original amount borrowed
is repaid by making equal payments
periodically.

𝑟
𝑃( )
R= ( 𝑚
𝑟 −𝑡𝑚 )
1−(1+ 𝑚
)

R = regular payment
P = present value of the loan
r = rate of interest
m = number of payments per year
t = time in years

Example 4
Find the monthly amortization for a Php
150, 000 debt which is to be repaid in 2
years at 7% interest compounded monthly.
Solution:
𝑟
𝑃( )
R=( )
𝑚
𝑟 −𝑡𝑚
1−(1+ 𝑚
)
P = 150, 000
t=2
r = 0.07
m = 12.
R=?
0.07
150, 000 ( )
R=( )
12
0.07 −(2)(12)
1−(1+ 12
)

R = Php 6, 715.80