Interest, Maturity, Future and Present Values in Simple Interest

Summary

This educational video script explains the concept of simple interest, using the formula IS=PRT to calculate interest, principal, rate, and time. It provides examples to demonstrate how to find each component when others are known. Additionally, it covers how to compute the maturity or future value by adding interest to the principal using the formula F=P(1+RT). The script aims to teach viewers these financial calculations in an accessible manner.

Takeaways

• 📚 The formula for calculating simple interest is IS = P * R * T, where IS is the simple interest, P is the principal amount, R is the interest rate, and T is the time in years.
• 🔍 To find the principal amount when the simple interest is known, use the formula P = IS / (R * T).
• 📈 The formula to determine the interest rate R when IS and P are known is R = IS / (P * T).
• ⏱️ When the time period is unknown, it can be calculated using T = IS / (P * R).
• 💹 The future or maturity value of an investment, where interest is added to the principal, is calculated by F = P * (1 + RT).
• 💡 An alternative way to find the future value is by adding the simple interest directly to the principal: F = P + IS.
• 💼 Example calculation: With a principal of 20,500 and a rate of 5% over 5 years, the simple interest is 5,125.
• 📊 To find the rate, divide the simple interest by the product of the principal and time, as shown in the example with a principal of 20,000, an interest of 5,000, and a time of 4 years, yielding a rate of 6.25%.
• 🕒 For determining time when given principal, interest, and rate, divide the simple interest by the product of the principal and rate, as demonstrated with a principal of 40,000, an interest of 700, and a rate of 7%, resulting in a time of 3 months.
• 🌐 A practical example of calculating the future value is given with a principal of 15,000, a rate of 2%, and a time of 4 months (one third of a year), resulting in a future value of 15,100.

Q & A

What is the formula for calculating simple interest?

The formula for calculating simple interest is I = P * R * T, where I is the simple interest, P is the principal amount, R is the simple interest rate, and T is the time in years.

How can you find the principal amount if you know the simple interest, rate, and time?

To find the principal amount, you can use the formula P = I / (R * T), where I is the simple interest, R is the rate, and T is the time.

What is the formula to determine the simple interest rate if you have the principal, interest, and time?

The formula to determine the simple interest rate is R = I / (P * T), where I is the simple interest, P is the principal, and T is the time.

How do you calculate the time when the principal, rate, and simple interest are known?

The time can be calculated using the formula T = I / (P * R), where I is the simple interest, P is the principal, and R is the rate.

What is the formula for finding the maturity or future value of an investment with simple interest?

The formula for finding the maturity or future value is F = P * (1 + RT), where F is the future value, P is the principal, R is the rate, and T is the time.

In the given example, what is the simple interest on a principal of 20,500 with a rate of 5% over 5 years?

The simple interest is calculated as 20,500 * 0.05 * 5, which equals 5,125 pesos.

How do you find the interest rate if you have the principal, simple interest, and time?

You can find the interest rate using the formula R = I / (P * T), where I is the simple interest, P is the principal, and T is the time.

In the example with a principal of 20,000, simple interest of 5,000, and a time of 4 years, what is the interest rate?

The interest rate is calculated as 5,000 / (20,000 * 4) = 0.0625 or 6.25%.

What is the time period for an investment with a principal of 40,000, simple interest of 700, and a rate of 7%?

The time period is calculated as 700 / (40,000 * 0.07) = 0.25 or one-fourth of a year, which is equivalent to three months.

How do you calculate the future value of an investment with a principal of 15,000, a rate of 2%, and a time of 4 months?

The future value is calculated as 15,000 * (1 + 0.02 * (4/12)) = 15,100 pesos.

What is an alternative method to calculate the future value of an investment?

An alternative method is to calculate the simple interest first, then add it to the principal. For example, with a principal of 15,000, a rate of 2%, and a time of 4 months, the simple interest is 15,000 * 0.02 * (4/12) = 100 pesos, and the future value is 15,000 + 100 = 15,100 pesos.

Outlines

00:00

📚 Simple Interest Calculations

This paragraph introduces the concept of simple interest and its calculation. The formula for simple interest is given as IS = PRT, where IS stands for simple interest, P is the principal amount, R is the rate of interest, and T is the time in years. The paragraph explains how to rearrange this formula to solve for unknowns such as the principal (P = IS/RT), the rate (R = IS/PT), and the time (T = IS/PR). Additionally, it discusses the concept of maturity or future value, which is the sum of the principal and the interest accrued, using the formula F = P(1 + RT). An example is provided to demonstrate the calculation of simple interest with given values for P, R, and T.

05:02

🔍 Examples of Finding Rate and Time in Simple Interest

The second paragraph delves into examples that demonstrate how to calculate the rate of interest and the time period when other variables are known. The first example calculates the rate using the formula R = IS/PT, where IS is the simple interest, P is the principal, and T is the time. The calculation results in a rate of 6.25% per year. The second example finds the time using the formula T = IS/PR, resulting in a time period of three months or one-fourth of a year. These examples illustrate the application of simple interest formulas to solve for different variables.

10:02

🌐 Future Value Calculations in Simple Interest

The third paragraph focuses on calculating the maturity or future value in a simple interest scenario. The formula F = P(1 + RT) is used to find the future value, which is the sum of the principal and the interest. An example is given with a principal of 15,000, an interest rate of 2%, and a time period of four months (one-third of a year). The calculation shows that the future value after four months is 15,100. An alternative method is also presented, where the simple interest is calculated first and then added to the principal to find the maturity value. Both methods yield the same result, confirming the accuracy of the calculations.

Keywords

💡Simple Interest

Simple interest is a calculation based on the principal amount of a loan or deposit, calculated as a percentage of the principal. It is defined as IS = PRT, where IS is the simple interest, P is the principal, R is the rate of interest, and T is the time in years. In the video, simple interest is used to demonstrate how to calculate the interest on an investment or loan over a period of time without compounding.

💡Principal

The principal refers to the initial amount of money invested or borrowed. In the context of the video, the principal is used in the formula for calculating simple interest (PRT) and is also the basis for determining the future value of an investment. The script provides an example where the principal is twenty thousand five hundred.

💡Interest Rate

The interest rate, denoted as 'r' in the script, is the percentage at which interest is charged on a loan or paid on a deposit. It is a key component in the formula for calculating simple interest. The video explains how to find the rate if the simple interest, principal, and time are known.

💡Time

Time, represented by 't' in the script, refers to the duration for which the principal amount is invested or borrowed. It is a crucial factor in the calculation of simple interest and is typically measured in years. The video script uses time to illustrate how the interest changes with different investment periods.

💡Future Value

Future value, or maturity value, is the amount of money the principal will grow to after a certain period, including interest. It is calculated using the formula F = P(1 + RT). The video provides an example where the future value is calculated by adding the interest to the principal amount.

💡Maturity Value

Maturity value is similar to future value and refers to the total amount of money accumulated at the end of the investment period, including both the principal and the interest earned. The script explains how to calculate maturity value using the formula F = P + IS, where IS is the simple interest.

💡Formula Manipulation

Formula manipulation involves altering the basic formula to solve for different unknowns. In the video, the simple interest formula PRT is manipulated to derive formulas for finding the principal (P = IS / RT), the rate (R = IS / PT), and the time (T = IS / PR). This demonstrates the flexibility of mathematical formulas in financial calculations.

💡Compound Interest

Although not the main focus of the video, compound interest is mentioned as a continuation from previous lessons. It is interest calculated on the initial principal, as well as any accumulated interest. The video script implies that the concepts explained for simple interest will be further explored in the context of compound interest in a future lesson.

💡Present Value

Present value refers to the current value of a future sum of money, given a specified rate of return. While not explicitly calculated in the script, the concept is alluded to when discussing the principal as the starting point for calculating future values or maturity values.

💡Investment

Investment is the act of committing money with the expectation of earning a return. The video script uses the context of investment to explain how simple interest is calculated and how it affects the growth of an investment over time.

💡Loan

A loan is money borrowed that must be repaid with interest. The script mentions loans in the context of calculating simple interest, emphasizing how the interest is computed on the borrowed amount over the term of the loan.

Highlights

Introduction to the discussion on interest maturity future and present values in simple interest.

Explanation of the simple interest formula: IS=PRT.

Formula for finding the principal amount when the simple interest is known.

Formula for finding the rate of interest when the simple interest is known.

Formula for finding the time when the simple interest is known.

Formula for calculating the maturity or future value of an investment.

Example calculation of simple interest with given principal, rate, and time.

Calculation of the interest rate using the formula R=IS/(P*T).

Example of finding the time period given principal, simple interest, and rate.

Conversion of decimal time to months and fraction of a year.

Example calculation of maturity value or future value with given principal, rate, and time.

Alternative method to calculate future value by adding simple interest to the principal.

Explanation of the relationship between principal, interest, and future value.

Emphasis on remembering the formulas for computing present value, interest, maturity value, and present value.

Anticipation of the next topic on computing interest maturity future value or maturity value and present values in compound interest.

Closing remarks and gratitude for the audience's attention.

Transcripts

[Music]

a pleasant morning to everyone today

we're going to discuss

interest maturity future and present

values in simple interest this is a

continuation of our previous lesson

about simple interest and compound

interest

so in computing the simple interests and

other related components the formula is

in simple interest or is is equals to p

r

t

where

so i s is simple interest

p is for the principal or the amount

invested or borrowed

or the present value

next we have the r

which is simple interest array and then

we have the t

or the time or term in years like i said

before

the time

is computed in years

so let's have

the formula that can be manipulated to

obtain the following relationships

so the formula for finding the principal

amount so it means the unknown is the

principal amount

we're going to use

p

is equals to simple interest divided by

r times t

so that is the formula in finding

the for the principal amount or the

principal value or the present value

then the formula for finding the rate

so we have the r

so the unknown is the rate so we have

the r is equals to is or the simple

interest

divided by

principle times the time

so next

the third formula is in finding the time

so the unknown now is the time

so t is equals to

simple interest divided by p

or principle times r or the rate

so these are the three formulas in

finding the unknown

if the unknown is not the simple

interest

okay

so

remember all those formulas

so let's

have

or let's have another formula in finding

the maturity or the future value

this maturity value is the amount where

in

where in the principal

is added to the interest or the interest

is added to the principal

so let's have the formula

so the future value value or the

maturity value is f

is equals to p

times 1

plus rt

so this is the formula in finding the

future

value or the maturity

value

or

we simply

future value

is equals to

price principle plus the simple interest

so this is what i said earlier

so the principal is added to the

interest or interest is added to the

principal

where f of course this is the maturity

or the future value

then the simple interest

is

and then the p

the principal or the amount invested or

borrowed or present value

and

r

is equals to simple interest rate and

the t is the time

or in term in years

so these are the formula in finding

the maturity value or the future value

so let's have an example

so given is the principal which is

twenty thousand five hundred

we have the rate

zero point zero five or

five percent

we have the t is equals to five it means

5 years

and then the unknown is the simple

interest

so first we have the solution

use the formula of simple interest

so simple interest is equals to the

principal times the rate times the time

so

substitute the value

to the formula

so i s

or simple interest is equals to twenty

20 500 the principal amount

times 0.05 which is the rate

and then times 5 which is the time in

years

so 20

500 times 0.05

times pipe you can use calculator in

computing

this one or in performing the operation

and we have

5125

pesos so the simple interest

in our example one

or in the given example is 5125

so therefore the simple interest is 5125

pesos

so let's have another example

so the gibbon are the principal which is

twenty thousand

the simple interest which is five

thousand

and the t is equals to four

then the unknown is the rate so we're

going to find the rate

so

here are the solution or here is the

solution

so

we're going to use the formula r is

equals to simple interest

over principle times time

or r is equals to is

divided by pp

then we're going to substitute the value

so five

the simple interest is 5000

and then the principal is 20 000

and then the time is four

so

you're going to perform the operation

so 5000 divide first 20 000

times 4 is equals to

80 000

and then 5000 divided by 80 000

we will have

0.0625

so this is in decimal form we can we can

convert the rate into percentage

so we have

6.25

so 0.0625 is equal to 6.25

therefore the rate of interest is 6.25

interest rate per year

okay next

let's have an example number three

we have the given

principle is equals to forty thousand

simple interest is seven hundred pesos

and the rate is seven percent

so we're going to find the time

or the unknown is the time

so here's the solution

so the formula the formula we're going

to use is t

is equals to simple interest times

principal

or sorry simple interest divided by

principal times rate

or t is equals to is divided by pr

so substitute the the given for the

given to the formula

so we have 700 which is the simple

interest

then 40 000 which is the principal

and the 0.07 which is the 7

order rate

and then perform the operation

so first you're going to multiply 40 000

to 0.07

and then you're going to perform 7 000

a 700 divided by the answer in the

multiplication or the product in 40 000

times

0.07

and then

we have

t is equals to

0.25 or point

25

now the time should be expressed in

the unit of time

so since

the time is expressed in years

so you're going to multiply

0.25

into 12

so that we get the unit of time in t

so 0.25

times 12 which is equivalent to 12

months in a year

so we will have three months

or

if you will you will convert

0.25 into fraction

so you're going to have

0.25

over

100

or 25 over 100

so

we'll have one

over

four

so one fourth of a year

so

the time

here

in the

in the given example we will have one

fourth of a year or three months

okay

so next

so therefore the term or time in years

is one part of a year or

three months

next

we have example number four the given

are

15 000 for the principal

t for the permanents

r is equals to two percent

and then we're going to find the

maturity value or the future value which

is the unknown f okay

when we say the maturity value or the

future value

this is interest

plus the principal or principal plus the

interest

okay first

we're going to use the formula in

finding the future value

is p

or the principle times one plus r

times t

okay then we're going to substitute the

value

so 15 000 which is the principal

then 1

plus

0.02

so in 2 percent we convert it to

decimal so two percent when we convert

is equal to zero point zero or point

zero two

and then we have the per month

since

i told you earlier or the p on the

previous lesson

the t is computed in years so if the

given

is 4 or in months

you're going to have your decimal or

your fraction

number or decimal number so in this case

we use one third of a year

now one third of a year because 4 over

12

when we simplify 4 over 12

so 4 divided by 4 is 1 then 12 divided

by 4 is 3 so we have 1 3.

okay

first

multiply 0.02 to

1 3.

so 0.02 times 1 third is equals to

point zero two over three

and then

we will have

fifteen thousand one hundred so you're

going to perform the operation

so again

so you're going first to multiply point

zero two to one third

which is equal to point zero two

now point zero two over

three and then

you add

the one to the answer or to the product

of this operation

and then after that you're going to

multiply 15 000

to the answer in this

operation

so

we will have

the future value of 15

100

pesos

so in four months

the future value is fifteen thousand one

hundred

so we have also the alternative solution

so simple interest

is equals to fifteen thousand times

point zero two times one third

and then we will have one hundred

pesos

so as a simple interest we will get one

hundred pesos this is also an

alternative solution

and then use the formula or the other

formula in computing the future value

which is principal plus

the simple interest

so

the principal is 15 thousand

and then the answer in computing the

simple interest is one hundred

and then we will have

the maturity value

fifteen thousand one hundred

so even though you use this formula or

this other formula

you can have the same answer

which is fifteen thousand one hundred

okay

so that's all for today

so i hope you learned how to compute the

present value the interest the maturity

value and the present value

so thank you for listening see you on

the next topic

in computing the interest maturity

future value or maturity value and the

present values in

compound interest

thank you and god bless