Assess Yourself

the interest rate and the accumulated interest on previous interest
the principal amount and the accumulated interest on previous interest
the principal amount, the interest rate, and the loan or investment term
the loan or investment term, the principal amount, and the accumulated interest over time

The formula to calculate simple interest is $I = Prt$ .

Compound interest involves interest on interest.
Compound interest involves the loan or investment term.
Compound interest involves the interest rate of the loan or investment.
Compound interest involves the initial amount of the loan or investment.

Since compound interest is compounded, interest will accumulate, not only from the principal, but also from previous interest.

the interest rate
the number of total years of the loan or investment
the number of times interest is compounded per year
the total amount paid or earned at the end of the term

Compound interest, as the name suggests, compounds the interest earned a certain number of times per year. This amount is multiplied by the time and divided into the interest rate.

$130
$20
$121
$107

In order to calculate the value of your investment after 2 years, divide the interest rate by the number of times the interest is compounded. Then add 1 to this value and raise it to a power that is the number of years of the investment multiplied by the number of times the interest is compounded. Finally, multiply this result by the principal amount to get the total amount.

the interest rate as a percentage
the interest rate as a decimal
the number of times the interest is compounded
the loan or investment term in years

In order to calculate simple interest, multiply the principal amount by the term in years. Next, multiply this result by the interest rate, which must be converted from a percentage to a decimal.

having a compound-interest investment earning 1% interest
having a compound-interest investment earning 5% interest
having a simple-interest investment earning 1% interest
having a simple-interest investment earning 5% interest

A compound-interest investment will earn more interest than one that uses simple interest.

How well do you understand the concepts and skills introduced in this lesson?

Assess Yourself

1. What is simple interest based on?

2. What is one difference between compound interest and simple interest?

3. In the compound interest formula $A = P\left( 1 + \frac{r}{n} \right)^{n \cdot t},$ what does the $n$ represent?

4. Use the compound interest formula $A = P\left( 1 + \frac{r}{n} \right)^{n \cdot t}$ to calculate the future value invested after two years on an initial amount of $100, with an interest rate of 10%, compounded annually.

5. In the simple interest formula $I = Prt$ , what does the $r$ represent?

6. Which of the following scenarios will be the most beneficial to you?

Summary

How well do you understand the concepts and skills introduced in this lesson?

Assess Yourself

1. What is simple interest based on?

2. What is one difference between compound interest and simple interest?

3. In the compound interest formula A=P(1+rn)n⋅t, A = P\left( 1 + \frac{r}{n} \right)^{n \cdot t}, what does the n n represent?

4. Use the compound interest formula A=P(1+rn)n⋅t A = P\left( 1 + \frac{r}{n} \right)^{n \cdot t} to calculate the future value invested after two years on an initial amount of $100, with an interest rate of 10%, compounded annually.

5. In the simple interest formula I=Prt I = Prt , what does the r r represent?

6. Which of the following scenarios will be the most beneficial to you?

Summary

3. In the compound interest formula $A = P\left( 1 + \frac{r}{n} \right)^{n \cdot t},$ what does the $n$ represent?

4. Use the compound interest formula $A = P\left( 1 + \frac{r}{n} \right)^{n \cdot t}$ to calculate the future value invested after two years on an initial amount of $100, with an interest rate of 10%, compounded annually.

5. In the simple interest formula $I = Prt$ , what does the $r$ represent?