Lesson Video: Simple Interest Mathematics • 7th Grade

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 “interest on interest.” For the purposes of this video, we’re only focusing on simple interest.

Simple interest can be calculated using the formula 𝐼 equals 𝑃 multiplied by 𝑅 multiplied by 𝑇. 𝐼 is the amount of interest. 𝑃 is the principal amount. This is the amount invested or borrowed. 𝑅 is the rate of interest written as a decimal. This will usually be given as a percentage in the question. 𝑇 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.

We’re 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 “of” 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 𝐼 equals 𝑃 multiplied by 𝑅 multiplied by 𝑇. 𝐼 is the amount of interest. 𝑃 is the principal amount, in this case, the amount deposited. 𝑅 is the interest rate written as a decimal. And 𝑇 is the amount of time. In this question, the amount deposited was 552 dollars. So, 𝑃 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 𝑅 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 Benjamin’s account if he makes no deposits or withdrawals for two years.

We can calculate the amount of simple interest accrued using the formula 𝐼 equals 𝑃 multiplied by 𝑅 multiplied by 𝑇. 𝐼 is the amount of interest that is accrued. 𝑃 is the principal amount, in this case, the amount that was invested. 𝑅 is the rate of interest written as a decimal. And finally, 𝑇 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, 𝑇 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 Benjamin’s 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, we’ll 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 𝐼 equals 𝑃 multiplied by 𝑅 multiplied by 𝑇. 𝐼 is the amount of interest earned, 𝑃 is the principal amount. This is the amount invested. 𝑅 is the rate of interest written as a decimal. And finally, 𝑇 is the amount of time. In this question, we know that the amount invested is 4,500 dollars. So, 𝑃 is equal to 4,500. The amount was deposited for five years. Therefore, 𝑇 is equal to five. The amount of interest that Jennifer earned was 765 dollars. So, this is the value of 𝐼. We’re trying to calculate the rate of interest 𝑅.

Substituting these values into the formula gives us 765 is equal to 4,500 multiplied by 𝑟 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 𝑟. Dividing both sides of this equation by 22,500 gives us 𝑟 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 𝐼 is equal to 𝑃 multiplied by 𝑅 multiplied by 𝑇. 𝐼 is the amount of interest earned. 𝑃 is the principal amount or the amount invested. 𝑅 is the rate of interest given as a decimal. And 𝑇 is the time period. In this question, we’re given information about account A and account B. We’re trying to calculate the amount that was invested in each account. Let’s let the amount invested in account A be 𝑥 dollars. As 10,000 dollars was invested altogether, the amount invested in account B is 10,000 minus 𝑥.

We’re 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, 𝑅 is equal to 0.08 and 0.05, respectively. As we’re only dealing with one year, the value for 𝑇 in both cases is one. Multiplying our three values for account A gives us 0.08𝑥. Therefore, the interest earned in account A is 0.08𝑥 dollars.

Repeating this process for account B gives us 𝐼 is equal to 0.05 multiplied by 10,000 minus 𝑥. Distributing the parentheses by multiplying 0.05 by 10,000 and then by negative 𝑥 gives us 500 minus 0.05𝑥. 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 0.08𝑥 plus 500 minus 0.05𝑥 is equal to 710. Grouping or collecting like terms on the left-hand side gives us 0.03𝑥 plus 500. Our next step is to subtract 500 from both sides of the equation. This gives us 0.03𝑥 is equal to 210. Finally, we divide both sides by 0.03. This gives us a value of 𝑥 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 𝐼 equals 𝑃 multiplied by 𝑅 multiplied by 𝑇. 𝐼 is the amount of interest earned. 𝑃 is the principal amount. This is the amount borrowed or invested. 𝑅 is the rate of interest, which we write as a decimal. Finally, 𝑇 is the time period for which the amount is invested.

As an example, let’s 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.