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GENMATH WEEK 11-20
Learning Activity 4
When invested at an annual rate of 5%, an amount earned Php 15,000.00
of simple interest in 2 years. How much money was initially invested?
The correct answer is: 150000
How much money should a student place in a time deposit in a bank that
pays 1.1% compounded annually so that he will have Php 200,000.00
after 6 yrs?
The correct answer is: 187293.65
Long Quiz 3
What interest rate per annum is a fund paying its clients if the third to
the last payment of a depositor became Php 510.05 from an initial
savings payment of Php 500.00?
The correct answer is: 12
When invested at an annual rate of 8%, an amount earned Php 24,000.00
of simple interest in 18 months. How much money was initially
invested?
The correct answer is: 200000
How long will Php 40,000.00 amount to Php 51,200.00 if the simple
interest rate is at 12% per annum?
Find the present value of Php 50,000.00 due in 4 years if money is
invested at 12% compounded semi-annually.
The correct answer is: 31370.62
What interest rate per annum is a fund paying its clients if the second to
the last payment of a depositor became Php 918.00 from an initial
savings payment of Php 900.00?
The correct answer is: 24
To what factor should you multiply a principal amount if you wish to
compute for the interest earned in 6 months of an investment in a fund
that pays 24% per annum?
The correct answer is: 12
Suppose Mrs. Reyes would like to save Php 1,000.00 at the end of each
month for 9 months in a fund that gives 5% per annum compounded
monthly. How much would the value of her savings be after 7 months?
(Hint: make sure the units of the interest rate and the term are the same)
The correct answer is: 7147.3
How long will Php 50,000.00 amount to Php 75,000.00 if the simple
interest rate is at 15% per annum?
Accumulate Php 15,000.00 for 2 years at 15% compounded monthly.
The correct answer is: 20210.27
How much do you need to save per month to have a future value of Php
10,146.00 after 12 months of saving in a fund that gives 12% per
annum?
The correct answer is: 800
How much should Kaye set aside and invest in a fund earning 2%
compounded quarterly if she needs Php 75,000.00 in 15 months?
The correct answer is: 73152.8
How many periods of artificial payments would you make if you are to
buy a commodity for quarterly payments of Php 8,000.00 for 8 years
starting two years from now?
The correct answer is: 7
Your teacher saves Php 5,000.00 every 6 months in a bank that pays
0.25% compounded monthly. How much will be her savings after 10
years?
The correct answer is: 101197.42
Your sister recently landed her dream job. As part of planning for future
expenses, she started to deposit Php 1,000.00 monthly in a fund that
pays 6% compounded quarterly. What is the equivalent interest?
The correct answer is: 0.004975
When invested at an annual rate of 7%, an amount earned Php 21,000.00
of simple interest in 3 years. How much money was initially invested?
The correct answer is: 100000
Learning Activity 6
A certain company gave out Php 25.00 dividend per share for its
common stock. The market value of the stock is Php 92.00. Determine
the stock yield ratio. (Note: Answer should be in percent with two
decimal places)
The correct answer is: 21.27
A land developer declared a dividend of Php 10,000,000.00 for its
common stock. Suppose there are 600,000 shares of common stock, how
much is the dividend per share?
The correct answer is: 16.67
Short Quiz 12
A property holdings declared a dividend of Php 9.00 per share for the
common stock. If the stock closes at Php 76.00, how large is the stock
yield ratio? (Note: Answer should be in percent with two decimal digits)
The correct answer is: 11.84
Find the amount of the semi-annual coupon for a Php 250,000.00 bond
which pays 7% convertible semi-annually for its coupons.
The correct answer is: 8750
A food corporation declared a dividend of Php 25,000,000.00 for its
common stock. Suppose there are 180,000 shares of common stock, how
much is the dividend per share? (Note: Answer should have two decimal
places.)
The correct answer is: 138.89
Determine the amount of a semi-annual coupon paid for a 3% -bond
with a face value of Php 80,000.00 which matures after 15 years. (Note:
Answer should have two decimal places)
The correct answer is: 1200
Learning Activity 5
Your sister recently landed her dream job. As part of planning for future
expenses, she started to deposit Php 1,000.00 monthly in a fund that
pays 6% compounded quarterly. How much will her funds worth be
after 15 years?
The correct answer is: 290076.28
How many months of artificial payments would you make if you are to
buy an appliance for Php 2,000.00 for 1 year starting from the 7th
month?
The correct answer is: 6
Short Quiz 11
Your sister recently landed her dream job. As part of planning for future
expenses, she started to deposit Php 1,000.00 monthly in a fund that
pays 6% compounded quarterly. What is the equivalent interest?
The correct answer is: 0.004975
Suppose Mrs. Reyes would like to save Php 1,000.00 at the end of each
month for 9 months in a fund that gives 5% per annum compounded
monthly. How much would the value of her savings be after 7 months?
(Hint: make sure the units of the interest rate and the term are the same)
The correct answer is: 7147.3
What interest rate per annum is a fund paying its clients if the second to
the last payment of a depositor became Php 918.00 from an initial
savings payment of Php 900.00?
The correct answer is: 24
How many periods of artificial payments would you make if you are to
buy a commodity for quarterly payments of Php 8,000.00 for 8 years
starting two years from now?
The correct answer is: 7
How long will Php 40,000.00 amount to Php 51,200.00 if the simple interest rate is at 12% per annum?
-2 years and 4 months
Find the present value of Php 50,000.00 due in 4 years if money is invested at 12% compounded semiannuall
The correct answer is: 31370.62
When invested at an annual rate of 7%, an amount earned Php 21,000.00 of simple interest in 3 years.
How much money was initially invested?
The correct answer is: 100000
Long Quiz 4
A Php 450,000.00 bond is redeemable at Php 550,000.00 after 5 years.
Coupons are given at 5% convertible semi-annually. Find the amount of
the semi-annual coupon.
The correct answer is: 11250
A family obtained a Php 1,000,000.00 mortgaged. If the monthly
payment is Php 38,000.00 for four years, how much is the total interest
paid?
The correct answer is: 824000
Find the amount of the semi-annual coupon for a Php 250,000.00 bond
which pays 7% convertible semi-annually for its coupons.
The correct answer is: 8750
Tell whether the following is a characteristic of stocks or bonds:
(a) A form of equity financing or raising money by allowing investors to be
part owners of the company. Answer (a) A form of debt financing, or
raising money by borrowing from investors. Answer
1(a). Stock
2(a). Bond
Determine the type of loan for the following:
If a condominium is purchased for Php 5,700,000.00 and the bank
requires 30% down payment, how much is the mortgaged amount?
The correct answer is: 3990000
A certain financial institution declared Php 57.00 dividend per share for
its common stock. The market value of the stock is Php 198.00.
Determine the stock yield ratio. (percentage with 2 decimal places)
The correct answer is: 28.79
For the purchase of a farm worth Php 2,800,000.00, the bank requires
30% down payment, find the mortgaged amount.
The correct answer is: 1960000
A business loan of Php 800,000.00 is to be repaid in full after 2 years.
What is the amount to be paid if the effective interest rate if 8%?
The correct answer is: 933120
Determine what type of loan is needed for the following situations:
A food corporation declared a dividend of Php 25,000,000.00 for its
common stock. Suppose there are 180,000 shares of common stock, how
much is the dividend per share? (Note: Answer should have two decimal
places.)
The correct answer is: 138.89
Mr. Capan obtained a 10-year mortgage for Php 4,200,000.00. If his
monthly payment is Php 39,500.00, how much is the total interest?
The correct answer is: 540000
Determine the amount of a semi-annual coupon paid for a 3% -bond
with a face value of Php 80,000.00 which matures after 15 years. (Note:
Answer should have two decimal places)
The correct answer is: 1200
Mr. Capan obtained a 10-year mortgage for Php 4,200,000.00. If his monthly payment is Php 39,500.00,
how much is the total interest?
The correct answer is: 540000
If a condominium is purchased for Php 5,700,000.00 and the bank requires 30% down payment, how
much is the mortgaged amount?
The correct answer is: 3990000
A family obtained a Php 1,000,000.00 mortgaged. If the monthly payment is Php 38,000.00 for four
years, how much is the total interest paid?
The correct answer is: 824000
Determine what type of loan is needed for the following situations
-Consumer loan
-Business loan
Learning Activity 8
Determine the truth value:
Consider the following scenario:
One Friday night, Roman and Malou are busy studying for their Logic
exam. Meanwhile, Hadji just tweeted a picture of himself eating crispy
pata and sisig. Jeff is sound asleep in his dorm room.
a. Either Roman has a date with Malou, or Jeff is sleeping or Hadji is
eating.
-True
b. Either Jeff is sleeping or Hadji is not eating.
-True
c. Roman and Malou are on a date and Jeff is sleeping, or Hadji is not
eating.
-False
Determine whether each of the following statements are propositions or
not. If the statement is a proposition, determine its truth value. (If it does
not have a truth value, put NA)
Statement
Proposition
Truth Value
1.Mindanao is an island in the Philippines.
2.Find a number which divides your age.
3.Help!
N
4.3 + 2 = 4
Y
Y
N
NA
FALSE
TRUE
NA
Short Quiz 14
Determine whether each of the following statements are propositions or
not. If the statement is a proposition, determine its truth value. (If it does
not have a truth value, put NA)
Statement
Proposition
Truth Value
1 f(x) = sqrt(x) / ( x+1 ) is a rational function.
Y
FALSE
2 What is the domain of the function?
N
NA
3 I am lying.
N
NA
4 It is not the case that sqrt(2) is a rational number. Y
TRUE
Determine the truth value:
Suppose that Abbey is in Grade 11.
a. If Abbey is in Grade 11, then she is a senior high school student.
-True
b. If Abbey is in Grade 11, then she is working as a lawyer.
-False
c. If Abbey has a degree in Computer Science, then she believes in true
love.
-True
Learning Activity 9
Determine which rule of inference is the basis for each of the argument
below:
Antonio Luna is a scientist.
Therefore, either Antonio Lune or Jose Rizal is a scientist.
-Addition
What is the rule of inference that was used in the argument in #1
-Modus Ponens
Determine which rule of inference is the basis for each of the argument
below:
Antonio Luna and Jose Rizal like Nelly Boustead.
Therefore, Antonio Lune likes Nelly Boustead.
-Simplification
Short Quiz 15
Determine whether each of the following arguments is valid or not.
a. If the solution turns blue litmus paper red, then the solution contains
acid. The solution does not contain acid. So, the solution does not turn
blue litmus paper red.
-Valid
b. If the solution turns blue litmus paper red, then the solution contains
acid. The solution turns blur litmus paper red, so the solution contains
acid.
-Valid
c. If you study hard, you refine your communication skills and build up
your confidence. If you refine your communication skills build up your
confidence, then your job opportunities increase. Hence, if you study
hard, your job opportunities increase.
-Valid
d. Kidnapping is wrong if society disapproves of it. Kidnapping is
wrong. So society disapproves of kidnapping.
-Invalid
e. If overeating causes disease, then it is not healthy. Overeating does
not cause disease. So overeating is healthy.
-Invalid
Learning Activity 10
Complete the proof of the argument below:
Proposition
Reason
1. s
Premise
2. ~(~s)
Double Negation
3. (~r) v (~s)
4. ~r
5. p
OR
6 p
Premise
2, 3, Disjunctive Syllogism
remise
4, 5, Disjunctive Syllogism
Short Quiz 16
Complete the proof of the argument below:
Proposition
Reason
1.(p OR r)
→ (~q)Premise
2.(~q)→ r
Premise
3.(p OR r) → r
Law of Syllogism
4.~r
Premise
5.~ (p OR r)
3, 4, Modus Tollens
What interest rate per annum is a fund paying its clients if the third to
the last payment of a depositor became Php 510.05 from an initial
savings payment of Php 500.00?
-12
Find the value of each logarithmic expression. (Note: There's only one
answer for the pair of logarithmic expressions indicated below.)
log2 (2^4/2^10)and log2 2^- log2 2^10
-5
To what factor should you multiply a principal amount if you wish to
compute for the interest earned in 6 months of an investment in a fund
that pays 24% per annum?
-12
Find the value of each logarithmic expression. (Note: There's only one
answer for the pair of logarithmic expressions indicated below.)
log7 75 and 5 · log7 7
-5
3(log9 x)2 = 6 log9 x
-False
Find the value of each logarithmic expression. (Note: There's only one
answer for the pair of logarithmic expressions indicated below.)
log7 (73 · 78) and log7 73 + log7 78
-11
(log3 2)(log3 4) = log3 6
-False
A Php 450,000.00 bond is redeemable at Php 550,000.00 after 5 years.
Coupons are given at 5% convertible semi-annually. Find the amount of
the semi-annual coupon.
-11250
How much do you need to save per month to have a future value of Php
10,146.00 after 12 months of saving in a fund that gives 12% per
annum?
-800
The horizontal line test is used to determine whether a function is oneto-one when its graph is given.
-True
Consider the rational function
p=(5,125,000V2−449,000V+19307)/(125V2(1,000V−43))p=(5,125,000
V2−449,000V+19307)/(125V2(1,000V−43)), does the function have a
p-intercept?
The relation pairing an SSS member to his/her SSS number is a one-toone function.
-True
The absolute value function has an inverse function.
-False
A certain financial institution declared Php 57.00 dividend per share for
its common stock. The market value of the stock is Php 198.00.
Determine the stock yield ratio. (percentage with 2 decimal places)
-28.79
A business loan of Php 800,000.00 is to be repaid in full after 2 years.
What is the amount to be paid if the effective interest rate if 8%?
-933120
Which of the is the inverse of (\f(x) = 5x - 4\)?
-(\f(x) = (x + 4)/5\)
(a) Mr. Lau wants to have another branch for his cellphone repair shop.
He decided to apply for a loan that can be used to pay for the rentals of
the new branch.
-Business Loan
(b) Mrs. Alon decided to take her family for a vacation. To cover the
expenses, she decided to apply for a loan.
-Consumer Loan
How much should Kaye set aside and invest in a fund earning 2%
compounded quarterly if she needs Php 75,000.00 in 15 months?
-73152.8
For the purchase of a farm worth Php 2,800,000.00, the bank requires
30% down payment, find the mortgaged amount.
-1960000
Fill in the table that represents the inverse of the function defined by:
-*Look at the pic in this folder*
Find the solution for the rational equation: ((2/(x+1)+5/2x)=2\).
How long will Php 50,000.00 amount to Php 75,000.00 if the simple
interest rate is at 15% per annum?
-3 years and 4 months
The set A = {(-4, 4), (-3, 2), (-2, 1), (0, -1), (1, -3), (2, -5)} of ordered pairs
form a function. Find the inverse of this function.
-*Look at the pic in this folder*
Complete the table of values below:
f(x)=(3)^x= -2
-4
-1
-2
0
0
1
2
2
3
4
6
Some functions have inverse functions.
-True
Suppose Mrs. Reyes would like to save Php 3,000.00 at the end of each
month for six months in a fund that gives 9% per annum compounded
monthly. How much would the value of her savings be after 6 months?
(Hint: make sure the units of the interest rate and the term are the same)
-426225
Mr. Santos received two offers on a lot that he wants to sell. Ms. Perez offered Php
50,000.00 down payment and a lump sum of Php 1,000,000.00 after 5 years. Mr. Castro
offered Php 50,000.00 down payment and Php 40,000.00 every quarter for 5 years.
Compare the market values of the two offer if the money can earn 5% compounded
annually.
A.1,050,000.00
B.9,000.00
C.The Php1,050,000.00
ind the unknown in the table below:Use Simple Interest Computation for your answers.
Principal (P)
Rate (r)
Time (t) (in years)
2%510,000.00360,000.00Answer
175,000.00880,000.009.25%2.5Answer
1. 12,000
2.35.29
or the function g(x) = 2x, find
g(2) = Answer
g(4) = Answer
g(0) = Answer
g(-2) = Answer
Interest (I) 10,000.008%15Answer
23,600.00500,000.0010.5%Answer
Answer
g(-4) = Answer
Mr. Abad got a Php 700,000.00 loan for the expansion of his business
payable monthly in 4 years. How much is the monthly amortization if the
interest rate is 12% compounded monthly?
18433.68
Which of the following represents an exponential function? Select one: a.
The number of trees in a rainforest b. population growth of microorganisms
c. The conversion of fahrenheit to celsius d. The amount billed to a girl who
bought a basket of flowers
Without using a calculator, find the value of the following logarithmic expression.
-3
Are the following functions one-to-one? (Answer by typing "Yes" or "No" - without the quotation
marks)
1. f(x)=4−3x4f(x)=4−3x4 Answer
2. f(x)=3−4xf(x)=3−4x Answer
3. f(x)=4−3x4−−−−−−√2f(x)=4−3x42 Answer
4. f(x)=3−4y4f(x)=3−4y4 Answer
5. f(x)=10f(x)=10 Answer
Without using a calculator, find the value of the following logarithmic expression.
log5 5
-1
Without using a calculator, find the value of the following logarithmic expression.
log7 1
-0
(log3 2)(log3 4) = log3 8 Select one: True False
A loan of Php 200,000.00 is to be repaid in full after 3 years. If the interest rate is 8% per
annum, how much should be paid after 3 years?
-251942.4
Determine the type of loan for the following:
(a) Mr. Lau wants to have another branch for his cellphone repair shop. He decided to apply
for a loan that can be used to pay for the rentals of the new branch. Answer
(b) Mrs. Alon decided to take her family for a vacation. To cover the expenses, she decided
to apply for a loan. Answer
A. Business loan
b. Personal loan
Determine what type of loan is needed for the following situations:
(a) Mr. Agustin plans to have a barbershop. He wants to borrow some money from the bank
in order for him to buy the equipment and furniture for the barbershop.
Answer: Business Loan
(b) Mr. and Mrs. Craig wants to borrow money from the bank to finance the college education
of their son.
Answer: Consumer Loan
Find the value of each logarithmic expression. (Note: There's only
one answer for the pair of logarithmic expressions indicated below.) log7
(73 · 78) and log7 73 + log7 78
-11
43 = x
-64
log1/2 16
-4
log2 32
=5
Find the value of each logarithmic expression. (Note: There's only one answer for the pair of
logarithmic expressions indicated below.)
log3 (27 · 81) and log3 27 + log3 81
-7
For the purchase of a house and lot worth Php 3,800,000.00, the bank requires 20% down
payment amount. Find the mortgaged amount.
-3040000
log3 2x2 = log3 2 + 2 log3 x
-false
log9 729
=3
log 22 = (log 2)2
=false
The relation pairing a real number to its square is a one-to-one function.
Select one:
True
log3 2x2 = 2 log3 2x
-false
Fill in the table that represents the inverse of the function defined by:
x -4 -3 -2 -1 0 1 2 3 4
y -9 -7 -5 -3 -1 1 3 5 7
(Pagpaliten mo lang value ng x at y )
(log3 2)(log3 4) = log3 6
Select one:
True
False
24 = x
=16
log7 (49/7) and log7 49 - log7 7
=1
3 log9 x2 = 6 log9 x
=true
GMAT-111
Learning Activity 4
How much money should a student place in a time deposit in a bank that pays 1.1% compounded
annually so that he will have Php 200,000.00 after 6 yrs?
The correct answer is: 187293.65
When invested at an annual rate of 5%, an amount earned Php 15,000.00 of simple interest in 2 years. How
much money was initially invested?
The correct answer is: 150000
GMAT-111 / ► Week 12: Key Concepts of Simple and Compound Inter... / ► Learning Activity 5
Your sister recently landed her dream job. As part of planning for future expenses, she started to
deposit Php 1,000.00 monthly in a fund that pays 6% compounded quarterly. How much will her
funds worth be after 15 years?
The correct answer is: 290076.28
How many months of artificial payments would you make if you are to buy an appliance for Php
2,000.00 for 1 year starting from the 7th month?
The correct answer is: 6
GMAT-111 / ► Week 12: Key Concepts of Simple and Compound Inter... / ► Short Quiz 11
Your sister recently landed her dream job. As part of planning for future expenses, she started to
deposit Php 1,000.00 monthly in a fund that pays 6% compounded quarterly. What is the equivalent
interest?
The correct answer is: 0.004975
How many periods of artificial payments would you make if you are to buy a commodity for quarterly
payments of Php 8,000.00 for 8 years starting two years from now?
The correct answer is: 7
Suppose Mrs. Reyes would like to save Php 1,000.00 at the end of each month for 9 months in a fund that
gives 5% per annum compounded monthly. How much would the value of her savings be after 7 months?
(Hint: make sure the units of the interest rate and the term are the same)
The correct answer is: 7147.3
What interest rate per annum is a fund paying its clients if the second to the last payment of a depositor became
Php 918.00 from an initial savings payment of Php 900.00?
The correct answer is: 24
A television set is for sale at Php 13,499.00 in cash or on installment terms,
Php 2,500.00 each month for the next 6 months at 9% compounded
annually.
=A. 14628.79
b. cash
A car dealer offers a 15% down payment for a purchase of a car. How
much is the mortgaged amount of the cash value of the car is Php
1,500,000.00?
=1275000
Determine what type of loan is needed for the following situations: (a) Mr.
Alonzo wants to have some improvements in their 10-year old house. He
wants to build a new room for their 13-year old daughter. He will borrow
money from the bank to finance this plan. Answer (b) Mr. Samson owns a
siomai food cart business. He wants to put another cart on a new mall in
the other city. He decided to have a loan to establish the new business.
Answer
=Consumer Loan
= Business Loan
Tell whether the following is a characteristic of stocks or bonds:
(a) A form of equity financing or raising money by allowing investors to be part owners of
the company. Answer
(a) A form of debt financing, or raising money by borrowing from investors. Answer
Stock
Bond