Interest, Maturity, Future and Present Values in Simple Interest
Summary
TLDRThis 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
- đ 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.
- đ To find the principal amount when the simple interest is known, use the formula P = IS / (R * T).
- đ The formula to determine the interest rate R when IS and P are known is R = IS / (P * T).
- â±ïž When the time period is unknown, it can be calculated using T = IS / (P * R).
- đč The future or maturity value of an investment, where interest is added to the principal, is calculated by F = P * (1 + RT).
- đĄ An alternative way to find the future value is by adding the simple interest directly to the principal: F = P + IS.
- đŒ Example calculation: With a principal of 20,500 and a rate of 5% over 5 years, the simple interest is 5,125.
- đ 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%.
- đ 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.
- đ 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
đ 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.
đ 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.
đ 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.
Mindmap
Keywords
đĄSimple Interest
đĄPrincipal
đĄInterest Rate
đĄTime
đĄFuture Value
đĄMaturity Value
đĄFormula Manipulation
đĄCompound Interest
đĄPresent Value
đĄInvestment
đĄLoan
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
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