### Video Transcript

In this video, we will solve word
problems involving simple interest in context. We will begin by looking at a definition
of simple interest.

There are two types of interest that we
regularly see: simple interest and compound interest. Simple interest is calculated on the
principal, or original, amount of a loan or investment. Compound interest, on the other hand, is
calculated on the principal amount and also on the accumulated interest of previous
periods. This is sometimes known as βinterest on
interest.β For the purposes of this video, weβre
only focusing on simple interest.

Simple interest can be calculated using
the formula πΌ equals π multiplied by π
multiplied by π. πΌ is the amount of interest. π is the principal amount. This is the amount invested or
borrowed. π
is the rate of interest written as a
decimal. This will usually be given as a
percentage in the question. π is the number of time periods, usually
in years as the interest rate is usually given per annum or per year. We will now look at some questions
involving simple interest.

A woman opened a bank account that
offered 20.7 percent interest per year. Given that she kept 6,000 Egyptian pounds
in the account for a year, find the total amount she has after the interest is added.

Weβre told in the question that the
interest rate of 20.7 percent is paid per year and that she kept the amount in her account
for one year. We can, therefore, calculate the amount
of simple interest that she accrued by working out 20.7 percent of 6,000 Egyptian
pounds. She invested 6,000 pounds, and the
interest rate was 20.7 percent. To convert a percentage into a decimal,
we divide by 100. When dividing by 100, all of our digits
move two places to the right. This means that 20.7 percent written as a
decimal is 0.207.

The word βofβ in mathematics means
multiply. We need to multiply 0.207 by 6,000. This is equal to 1242. 20.7 percent of 6,000 Egyptian pounds is
1,242 Egyptian pounds. As this is the interest accrued, we can
calculate the total amount that she has in her account by adding this to 6,000. After one year, the woman has 7,242
Egyptian pounds in her account.

The next question that we look at
involves using the simple interest formula.

Find the simple interest earned in a
savings account given that 552 dollars is deposited for seven months with an interest rate
of 16.5 percent per year.

The amount of simple interest can be
calculated using the formula πΌ equals π multiplied by π
multiplied by π. πΌ is the amount of interest. π is the principal amount, in this case,
the amount deposited. π
is the interest rate written as a
decimal. And π is the amount of time. In this question, the amount deposited
was 552 dollars. So, π equals 552. The interest rate was 16.5 percent per
year. We can convert any percentage into a
decimal by dividing by 100. This means that the value of π
is
0.165.

The interest rate was per year, and we
deposited the amount for seven months. As there are 12 months in a year, the
time in this case is equal to seven twelfths. We can, therefore, calculate the simple
interest by multiplying 552 by 0.165 by seven twelfths. This is equal to 53.13. The amount of interest earned is 53
dollars and 13 cents.

Our next question is a slightly more
complicated problem using the same formula.

Benjamin had 820,000 dollars. He paid 250,000 dollars in taxes and
invested the rest in a savings account with a 4.95 percent simple interest. Determine the amount of money in
Benjaminβs account if he makes no deposits or withdrawals for two years.

We can calculate the amount of simple
interest accrued using the formula πΌ equals π multiplied by π
multiplied by π. πΌ is the amount of interest that is
accrued. π is the principal amount, in this case,
the amount that was invested. π
is the rate of interest written as a
decimal. And finally, π is the time period. In this question, the amount invested can
be calculated by subtracting the amount of tax, 250,000, from 820,000. This is equal to 570,000. Therefore, Benjamin invested 570,000
dollars.

The rate of interest was 4.95
percent. We can convert this to a decimal by
dividing by 100. This is equal to 0.0495. As we want to calculate the amount of
money after two years, π is equal to two. We can, therefore, calculate the amount
of simple interest by multiplying 570,000, 0.0495, and two. Typing this into the calculator gives us
56430. The amount of interest that Benjamin
accrued was 56,430 dollars. As we need to calculate the new amount of
money in Benjaminβs account, we need to add this interest to 570,000, the amount he
initially invested. 570,000 plus 56,430 is equal to
626,430. We can, therefore, conclude that, after
two years, Benjamin has 626,430 dollars.

In the next question, weβll be given the
amount of interest earned, and we will need to calculate the rate of interest.

If Jennifer invested 4,500 dollars in a
certificate of deposit for five years and earned 765 dollars, determine the rate of
interest.

In order to calculate the amount of
interest earned, we can use the formula πΌ equals π multiplied by π
multiplied by π. πΌ is the amount of interest earned, π
is the principal amount. This is the amount invested. π
is the rate of interest written as a
decimal. And finally, π is the amount of
time. In this question, we know that the amount
invested is 4,500 dollars. So, π is equal to 4,500. The amount was deposited for five
years. Therefore, π is equal to five. The amount of interest that Jennifer
earned was 765 dollars. So, this is the value of πΌ. Weβre trying to calculate the rate of
interest π
.

Substituting these values into the
formula gives us 765 is equal to 4,500 multiplied by π multiplied by five. As multiplication is commutative, we can
multiply 4,500 by five first. The equation simplifies to 765 is equal
to 22,500 multiplied by π. Dividing both sides of this equation by
22,500 gives us π is equal to 0.034. To convert from a decimal to a
percentage, we multiply by 100. This moves all of the digits two places
to the left, and the interest rate is 3.4 percent. 4,500 dollars invested for five years at
3.4 percent simple interest per year would earn 765 dollars.

The final question we will look at in
this video compares two accounts and involves using linear equations.

At the beginning of a year, you invested
10,000 dollars into two accounts, A and B, which receive eight percent simple interest and
five percent simple interest, respectively. At the end of that year, you had 10,710
dollars in your combined accounts. How much was invested in each
account?

In order to answer this question, we
firstly need to consider the simple interest formula. This states that πΌ is equal to π
multiplied by π
multiplied by π. πΌ is the amount of interest earned. π is the principal amount or the amount
invested. π
is the rate of interest given as a
decimal. And π is the time period. In this question, weβre given information
about account A and account B. Weβre trying to calculate the amount that
was invested in each account. Letβs let the amount invested in account
A be π₯ dollars. As 10,000 dollars was invested
altogether, the amount invested in account B is 10,000 minus π₯.

Weβre told that the interest rate for
account A was eight percent. For account B, this was five percent. To convert from a percentage to a
decimal, we divide by 100. So, π
is equal to 0.08 and 0.05,
respectively. As weβre only dealing with one year, the
value for π in both cases is one. Multiplying our three values for account
A gives us 0.08π₯. Therefore, the interest earned in account
A is 0.08π₯ dollars.

Repeating this process for account B
gives us πΌ is equal to 0.05 multiplied by 10,000 minus π₯. Distributing the parentheses by
multiplying 0.05 by 10,000 and then by negative π₯ gives us 500 minus 0.05π₯. At the end of the year, we were told we
have 10,710 dollars in the combined accounts. The total interest earned can, therefore,
be calculated by subtracting 10,000 from 10,710. This is equal to 710 dollars. We will now clear some space to solve the
equations.

We know that the total interest from
account A and account B is equal to 710. Writing this as an equation, we have
0.08π₯ plus 500 minus 0.05π₯ is equal to 710. Grouping or collecting like terms on the
left-hand side gives us 0.03π₯ plus 500. Our next step is to subtract 500 from
both sides of the equation. This gives us 0.03π₯ is equal to 210. Finally, we divide both sides by
0.03. This gives us a value of π₯ equal to
7,000. This was the amount invested in account
A, 7000 dollars. As the total amount invested was 10,000
dollars, then the amount invested in account B was 3,000 dollars.

Investing these amounts in two accounts
with simple interest rates of eight percent and five percent for one year would accrue 710
dollars of interest. 560 dollars of these would come from
account A as 0.08 multiplied by 7,000 is 560. This means that 150 dollars would come
from account B as 710 minus 560 is 150.

We will now summarize the key points from
this video. Simple interest is calculated on the
principal, or original, amount of a loan or investment. We can calculate the amount of interest
earned using the formula πΌ equals π multiplied by π
multiplied by π. πΌ is the amount of interest earned. π is the principal amount. This is the amount borrowed or
invested. π
is the rate of interest, which we
write as a decimal. Finally, π is the time period for which
the amount is invested.

As an example, letβs assume that we
invested or borrowed 6,000 dollars at 4 percent simple interest per year for five years. The simple interest can be calculated by
multiplying 6,000 by 0.04 by five. This is equal to 1,200. The interest accrued in that five-year
period was 1,200 dollars.