Mathematics of Investment - Simple Interest - Simple Interest Formula (Topic 1)

Summary

This 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

• 📚 The course 'Mathematics of Investments' is structured into four main parts: interest, depreciation, and bonds, with a focus on the first part about interest.
• 💰 Interest is defined as the money paid for the use of borrowed money, highlighting the concept of simple and compound interest.
• 🔢 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.
• 🚀 Compound interest is calculated on the initial principal plus any accumulated interest, making it a more complex concept than simple interest.
• 🌐 The future amount (\( F \)) is the total sum when interest is added to the principal at the end of a stipulated time, calculated as \( F = P + I \).
• 📝 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.
• 💼 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.
• 📉 Another example involves calculating the interest rate for an investment that earned 6500 after three years, using the simple interest formula.
• 📈 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.
• 📊 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.
• 🏦 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.
• 📋 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

00:00

📚 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.

05:04

🔢 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.

10:05

🏦 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.

Keywords

💡Interest

Interest is the money paid for the use of borrowed money or earned on deposited money. It is a fundamental concept in the field of finance and investment. In the video, interest serves as the central theme, with the script explaining two types of interest: simple and compound. The script uses the term to introduce the basic formula for calculating interest and provides examples of how it is applied in different financial scenarios.

💡Simple Interest

Simple interest is calculated on the principal amount only and does not take into account any additional interest on interest. It is a straightforward concept that is essential for understanding more complex financial calculations. The video script defines simple interest and uses it in various examples, such as calculating the interest Venus earns on her bank deposit or determining the rate at which Christian's investment earns interest.

💡Compound Interest

Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. It is a more complex form of interest that can significantly affect the growth of an investment over time. Although the script does not delve into compound interest in detail, it contrasts it with simple interest to highlight the difference in how interest is calculated.

💡Principal

The principal refers to the initial amount of money that is deposited in a bank, invested, or borrowed. It is the base amount on which interest is calculated. The script consistently uses the term 'principal' in its examples to illustrate the starting point for calculating simple interest, such as in the case of Venus's bank deposit or Lena's bank loan.

💡Rate of Interest

The rate of interest is the percentage at which interest is paid or earned on the principal amount. It is a critical factor in determining the amount of interest that will be accrued over time. The script explains the rate of interest in the context of the simple interest formula and uses it in examples to calculate the interest earned or the rate at which an investment grows.

💡Future Amount

The future amount is the total sum of the principal and the interest earned over a certain period. It represents the total amount that will be available after the interest has been added to the principal. The script introduces the concept of the future amount and uses it in the formula to calculate the total amount that will be due or received at the end of a specified time, such as in the case of Vincent's loan repayment.

💡Formula

A formula in the context of the video refers to the mathematical expressions used to calculate simple interest, the future amount, and other related financial values. The script presents several formulas, such as I = P * R * T for simple interest, and uses them to solve various financial problems presented in the examples.

💡Investment

Investment in the video refers to the act of committing money with the expectation of earning a return or profit. It is a key concept in the study of finance and is used in the script to illustrate how simple interest can be earned on investments, as seen in the example of Christian's stock market investment.

💡Loan

A loan is money borrowed from a bank or other financial institution that is expected to be repaid with interest. The script discusses loans in the context of simple interest, showing how the formula can be used to calculate the total amount to be repaid, including interest, as demonstrated in Lena's and Vincent's examples.

💡Deposit

A deposit is money placed into a bank or other financial account, often to earn interest. The script uses the term 'deposit' in the context of Venus's bank deposit example, where she earns simple interest on the amount she has deposited.

💡Time

Time, in the context of the video, refers to the duration for which money is invested, borrowed, or deposited. It is a crucial component in the calculation of simple interest, as the amount of interest earned is directly related to the length of time the money is invested or borrowed. The script consistently includes 'time' as a variable in the simple interest formula and examples, such as the two-year period for Venus's deposit or the three-year period for Christian's investment.

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