Mathematics of Investment - Simple Interest - Simple Interest Formula (Topic 1)
Summary
TLDRThis script offers an in-depth exploration of the mathematics of investments, focusing on the concept of interest. It explains the difference between simple and compound interest, detailing the formula for calculating simple interest (I = P * R * T) and how to determine the future amount of a loan or investment. The script provides several examples to illustrate the calculation of interest, the rate of interest, and the original loan amount, making the topic accessible and practical for learners.
Takeaways
- π The course 'Mathematics of Investments' is structured into four main parts: interest, depreciation, and bonds, with a focus on the first part about interest.
- π° Interest is defined as the money paid for the use of borrowed money, highlighting the concept of simple and compound interest.
- π’ Simple interest is calculated only on the principal amount, with the formula being \( I = P \times R \times T \), where \( I \) is the interest, \( P \) is the principal, \( R \) is the rate, and \( T \) is the time.
- π Compound interest is calculated on the initial principal plus any accumulated interest, making it a more complex concept than simple interest.
- π The future amount (\( F \)) is the total sum when interest is added to the principal at the end of a stipulated time, calculated as \( F = P + I \).
- π The formula for the future amount considering simple interest is \( F = P \times (1 + RT) \), which can also be rearranged to solve for the principal amount.
- πΌ An example is given where Venus deposited 5000 at a 6.5% simple interest rate for two years, illustrating the calculation of simple interest earned.
- π Another example involves calculating the interest rate for an investment that earned 6500 after three years, using the simple interest formula.
- π The length of time for which money is borrowed can be determined using the simple interest formula, as shown in an example where Lena borrowed 10,000 at a 12% simple interest rate.
- π The original loan amount can be calculated if the total interest paid is known, demonstrated with Rachel's loan example where she paid 7400 in interest over four years.
- π¦ Vincent's example of borrowing 35,000 at a 12.5% simple interest rate for five years shows how to calculate the total amount to be paid back, including interest.
- π The final example involves calculating the original loan amount when the total amount paid back is known, using the simple interest formula to find the principal.
Q & A
What is the definition of interest according to the script?
-Interest is defined as the money paid for the use of borrowed money or deposited money.
What are the two types of interest mentioned in the script?
-The two types of interest mentioned are simple interest and compound interest.
What is the formula for calculating simple interest?
-The formula for calculating simple interest is I = P * R * T, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period.
What is the future amount in the context of simple interest?
-The future amount is the total sum of the principal amount plus the interest earned when the interest is added to the principal at the end of the stipulated time.
How can you find the principal amount if you know the future amount, rate, and time?
-You can find the principal amount by dividing the future amount by (1 + R * T).
In the example, how much interest did Venus earn after depositing 5000 at a 6.5% simple interest rate for two years?
-Venus earned 650 pesos in interest after two years.
What rate of interest did Christian's investment earn if it guaranteed an interest of 6500 after three years with a principal of 30,000?
-Christian's investment earned at a rate of 6.22%.
If Lena borrowed 10,000 at a 12% simple interest rate and paid 4500 at the end of the term, how long did she use the money?
-Lena used the money for 3.75 years.
What was the original loan amount if Rachel paid 7400 in interest at a 14.5% rate for a four-year loan?
-The original loan amount was 12,758.62 pesos.
How much will Vincent pay the bank after five years if he borrowed 35,000 at a 12.5% simple interest rate?
-Vincent will pay a total of 56,875 pesos after five years.
If the total amount paid on a loan is 84,000 pesos for two years at a 9% simple interest rate, what was the original loan amount?
-The original loan amount was 71,186.44 pesos.
Outlines
π Introduction to the Mathematics of Investments
This paragraph introduces the course 'Mathematics of Investments', which is structured into four main parts: interest, depreciation, and bonds. The focus of the first part is on interest, which is defined as the money paid for the use of borrowed or deposited money. The paragraph explains the difference between simple and compound interest, where simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any accumulated interest. The simple interest formula (I = P * R * T) is introduced, along with the future amount formula (F = P + I), and an example is provided to illustrate the calculation of simple interest.
π’ Calculation Examples for Simple Interest
This paragraph delves into various examples to demonstrate the application of the simple interest formula. It covers scenarios such as calculating the interest earned on a bank deposit, determining the interest rate for an investment based on a guaranteed return, figuring out the duration of a loan given the total amount paid, and calculating the original loan amount based on the interest paid. Each example provides a step-by-step calculation process, illustrating how to use the simple interest formula (I = P * R * T) to solve different financial problems.
π¦ Advanced Simple Interest Calculations and Conclusion
The final paragraph presents more complex examples of simple interest calculations, including determining the total amount to be paid back after a certain period and finding the original loan amount given the total amount paid with interest. It also touches on converting months into years for interest calculations. The paragraph concludes with a summary of the simple interest formula and an invitation for questions, emphasizing the importance of understanding the concepts taught in the course.
Mindmap
Keywords
π‘Interest
π‘Simple Interest
π‘Compound Interest
π‘Principal
π‘Rate of Interest
π‘Future Amount
π‘Formula
π‘Investment
π‘Loan
π‘Deposit
π‘Time
Highlights
Introduction to the Mathematics of Investments course, covering topics such as interest, depreciation, and bonds.
Definition of interest as money paid for the use of borrowed or deposited money.
Explanation of the two types of interest: simple and compound.
Simple interest is calculated only on the principal amount.
Compound interest is calculated on the principal plus any accumulated interest.
Simple interest formula: I = P * R * T.
Future amount formula when interest is added to the principal.
Example calculation of simple interest earned on a bank deposit.
Example determining the interest rate from an investment return.
Calculation of the time duration for a loan given the interest paid.
Determination of the original loan amount given the total interest paid over a period.
Example of calculating the total amount to be paid back on a loan after a certain period.
Explanation of converting months into years for interest calculations.
Calculation of the future amount when a loan is paid off after a specified term.
Determination of the original loan amount given the total amount paid including interest.
Invitation for questions and comments to engage with the audience.
Transcripts
welcome to mathematics of investments so
supports nothing at all
course topics
so for part one we are going to tackle
about interest
part two and we d part three
depreciation and part four about the
bonds so the first one is about the
interest
so what is interest interest it says
here that interest is the money paid for
the use of the borrowed
money so
of course
borrowed money and deposited money on my
interest
on so there are two kinds of interest
the simple and compound
interest so
the simple interest is the interest paid
on the principal
money length only is called the simple
interest in comparison amanda's compound
interest
when simple interest that is ju is not
paid the amount is added to the interest
bearing principle
the interest calculated on this new
principle is called
the compound interest so simple interest
very simple
my formula tayo mamaya at the interest
paid
is for the moneylent lang talaga when
some pound interest
[Music]
interest so mass complexion concept and
compound interest case is a simple
interest
okay so this is uh
going to be our topics under the simple
interest so for two weeks we are going
to discuss about
these topics these six topics so the
first topic is the simple interest
formula
the formula for the simple interest is i
equal to p times r times t where the i
is the simple interest the p
is the principal amount in coordinate
position
the r is the rate of interest percentage
interest
[Music]
when interest is added to the principle
at the end of the stipulated time the
total sum is called the future amount or
f
so the future amount is equal to the p
or the principal amount plus the
interest so
combining the value of the interest
plus the principal amount you knew
all in all babayaranko within the
certain period of
time so combining the two formula
we have f equals p times prt since i
is equal to prt then factoring in
[Music]
f is equal to p times one plus rt
and finding for the value of p that is
equal to f
divided by one plus r t
so for example venus deposited 5000
in the bank at 6.5 simple interest for
two years how much will she earn after
two years
assuming that no withdrawals were made
okay so young given atenjan your
principal amount nah the deposit in
venus is five thousand pesos
the r is the six point five percent or
zero point zero
six five gasoline 6.5 divided by 100
that is 0.65 calcium point zero sixty
five at the young is a substitute
nothing
formula so the t or the length of time
is within two years how much is the
interest
okay so using the simple
interest formula i equals p times r
times t
substituting for all the values p is
five thousand
r is point zero six five times two
that is equal to six hundred fifty pesos
interest okay so five
five thousand adding positive venus a
banco
[Music]
650 pesos
so another example christian invested 30
000 in the stock market which guaranteed
an interest of 6500 after three years
at what rate would her inverse
investment
earn so nothing dito
or the length of time is three years
then you i
is the interest six thousand and
five hundred so what is the value of
r so using the simple interest formula
again
[Music]
for r we have to divide both sides by
p and d parameter
so the r is equal to i over
p t so substituting
within a time of substituting values
i is six thousand five hundred p is 30
000
then three the r is 0.622
or 6.22
another example lena borrowed 10 000
from a bank charging
12 simple interest with a promise that
she would pay the principal and
interest at the end of the agreed term
if she paid 4
500 at the end of the specified term how
long did she use the money
so how long did she use the money
is the length of time so given 10 000 as
the principal amount young r
is 12 or 0.12 then i
is 4 and hundred using the simple
interest formula again i equals prt
since p young unknown either divide not
in both sides by
p r paramagang p and chaka r
soy value now is equal to i
over pr substitute
i is ten thousand i mean i
is four thousand five hundred p is ten
thousand
and r is point so the t is
3.75 years
okay for the next example rachel paid
7 400 interest at 14.5 percent for a
four year
loan what was the original loan
original meaning
so given r is 14.5 percent
t is four years i is seven thousand four
hundred
using the simple interest formula again
[Music]
since p unknown or your principal amount
we have to divide both sides of the
equation by r
and t so your equivalent
volume p is i over rt
p equals i over rt substituting for
those values
i is 7 400 r is 0.145
then t is 4 that is equal to 12
758 and 62
centavos
[Music]
okay
then next example vincent var borrowed
35 000 from about a 12.5 simple interest
for five years how much will she pay the
the bank
after five years so
we are going to compute for the future
amount or
f
[Music]
after five years
so given young principal amount is 35
000
r is 12.5 percent t is 5 years
interest amount
using the simple interest formula
i is equal to prt in order to get the
value of i
substituting the 35 000 the point one
two five and the five years
that interest is equal to twenty one
thousand eight hundred seventy five
pesos
so using this i
[Music]
and the principal amount p predicted
in order to get the value of the future
amount or f
so p is 35 000 i is 21 875 you know
10 so f therefore is equal to 50
56 875
pesos
next if rose borrowed 40 000
from a bank at 10.5 simple interest how
how much will she pay at the end of 15
months
[Music]
in years equivalent nothing in in years
in 15 months is 1.25 years or one and
one-fourth
a year so anonymous f
in order to find for the value of f
gagamite native
formula f equals p times one
plus rt
is always in years on unit in d
months in the days in the years
so the value for f is equal to 42
000 times 1 plus 0.105 times 1.25
so the resulting
value 4.125 times 1.25
is 0.13125 using the pemdas rule
so f is equal to 42 000 times 1.13125
so f now is equal to forty seven
thousand four hundred
five hundred twelve and fifty centavos
next example the total amount paid on a
loan is eighty four thousand pesos if
the loan was for two years
at nine percent simple interest what was
the original loan
okay um
given you f okay in future amount
total amount paid salon 84
000 yuan or nothing is nine percent or
zero point zero nine in decimal
young tina then is two years
so using your formula nothing
now since then we have to divide the
equation both sides by
one plus rt so we can get p
is equal to f over one plus rt
okay substituting for the value of f
r and t eighty-four thousand times one
plus point zero nine
times two or
point eighteen since point o nine times
two is point eighteen
one plus point eighteen is one point
eighteen
so the principal amount is seventy one
thousand one hundred eighty six
pesos and forty four centavos
so that is for the sub topic simple
interest formula under the simple
interest
topic so if you have any questions just
comment down
okay so thank you for listening
Browse More Related Video
Aptitude Preparation for Campus Placements #10 | Simple Interest | Quantitative Aptitude
ANUITAS
Formula for continuously compounding interest | Finance & Capital Markets | Khan Academy
Anuitas | Matematika kelas XI SMA/SMK Kurikulum Merdeka
ILLUSTRATING SIMPLE AND COMPOUND INTEREST || GRADE 11 GENERAL MATHEMATICS Q2
Pay Off Car Loan FASTER
5.0 / 5 (0 votes)