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Solve Simple Interest Applications

Use the simple interest formula

Use the Simple Interest Formula

Do you know that banks pay you to let them keep your money? The money you put in the bank is called the principal, $P,$ and the bank pays you interest, $I.$ The interest is computed as a certain percent of the principal; called the rate of interest, $r.$ The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent. The variable for time, $t,$ represents the number of years the money is left in the account.

The formula we use to calculate simple interest is $I=Prt.$ To use the simple interest formula we substitute in the values for variables that are given, and then solve for the unknown variable. It may be helpful to organize the information by listing all four variables and filling in the given information.

Example

Try it.

Find the simple interest earned after $3$ years on $\text{\$500}$ at an interest rate of $\text{6\%.}$

Solution

Organize the given information in a list.

$\begin{array}{lll}I & = & ? \\ P & = & \text{\$500} \\ r & = & \text{6\%} \\ t & = & \text{3 years}\end{array}$

We will use the simple interest formula to find the interest.

Write the formula.	$I=Prt$
Substitute the given information. Remember to write the percent in decimal form.	$I=(500)(0.06)(3)$
Simplify.	$I=90$
Check your answer. Is $90 a reasonable interest earned on $500 in 3 years?
In 3 years the money earned 18%. If we rounded to 20%, the interest would have been 500(0.20) or $100. Yes, $90 is reasonable.
Write a complete sentence that answers the question.	The simple interest is $90.

In the next example, we will use the simple interest formula to find the principal.

Now we will solve for the rate of interest.

Condensed — the full section is in OpenStax Prealgebra 2e.

Solve Simple Interest Applications

Applications with simple interest usually involve either investing money or borrowing money. To solve these applications, we continue to use the same strategy for applications that we have used earlier in this chapter. The only difference is that in place of translating to get an equation, we can use the simple interest formula.

We will start by solving a simple interest application to find the interest.

Example

Try it.

Nathaly deposited $\text{\$12,500}$ in her bank account where it will earn $\text{4\%}$ interest. How much interest will Nathaly earn in $5$ years?

Solution

We are asked to find the Interest, $I.$

Organize the given information in a list.

$\begin{array}{lll}I & = & ? \\ P & = & \text{\$12,500} \\ r & = & \text{4\%} \\ t & = & \text{5 years}\end{array}$

Write the formula.	$I=Prt$
Substitute the given information.	$I=(12,500)(0.04)(5)$
Simplify.	$I=2,500$
Check your answer. Is $2,500 a reasonable interest on $12,500 over 5 years?
At 4% interest per year, in 5 years the interest would be 20% of the principal. Is 20% of $12,500 equal to $2,500? Yes.
Write a complete sentence that answers the question.	The interest is $2,500.

There may be times when you know the amount of interest earned on a given principal over a certain length of time, but you don't know the rate. For instance, this might happen when family members lend or borrow money among themselves instead of dealing with a bank. In the next example, we'll show how to solve for the rate.

Example

Try it.

Loren lent his brother $\text{\$3,000}$ to help him buy a car. In $\text{4 years}$ his brother paid him back the $\text{\$3,000}$ plus $\text{\$660}$ in interest. What was the rate of interest?

Solution

We are asked to find the rate of interest, $r.$

Organize the given information.

$\begin{array}{lll}I & = & 660 \\ P & = & \text{\$3,000} \\ r & = & ? \\ t & = & \text{4 years}\end{array}$

Write the formula.	$I=Prt$
Substitute the given information.	$660=(3,000)r(4)$
Multiply.	$660=(12,000)r$
Divide.	$\frac{660}{12,000}=\frac{(12,000)r}{12,000}$
Simplify.	$0.055=r$
Change to percent form.	$\text{5.5\%}=r$
Check your answer. Is 5.5% a reasonable interest rate to pay your brother?
$I=Prt$
$660\overset{?}{=}(3,000)(0.055)(4)$
$660=660✓$
Write a complete sentence that answers the question.	The rate of interest was 5.5%.

Condensed — the full section is in OpenStax Prealgebra 2e.

Key Concepts

Simple interest
- If an amount of money, $P$, the principal, is invested for a period of $t$ years at an annual interest rate $r$, the amount of interest, $I$, earned is $I=Prt$
- Interest earned according to this formula is called simple interest.

Solve Simple Interest Applications

Use the Simple Interest Formula

In the following exercises, use the simple interest formula to fill in the missing information.

Try it.

Interest	Principal	Rate	Time (years)
	$\text{\$1200}$	$\text{3\%}$	$5$

Solution

$180

Try it.

Interest	Principal	Rate	Time (years)
	$\text{\$1500}$	$\text{2\%}$	$\text{4}$

Try it.

Interest	Principal	Rate	Time (years)
$\$4410$		$\text{4.5\%}$	$\text{7}$

Solution

$14,000

Try it.

Interest	Principal	Rate	Time (years)
$\$2112$		$\text{3.2\%}$	$\text{6}$

Try it.

Interest	Principal	Rate	Time (years)
$\$577.08$	$\text{\$4580}$		$\text{2}$

Solution

6.3%

Try it.

Interest	Principal	Rate	Time (years)
$\$528.12$	$\text{\$3260}$		$\text{3}$

In the following exercises, solve the problem using the simple interest formula.

Try it.

Find the simple interest earned after $5$ years on $\text{\$600}$ at an interest rate of $\text{3\%.}$

Solution

$90

Try it.

Find the simple interest earned after $4$ years on $\text{\$900}$ at an interest rate of $\text{6\%.}$

Try it.

Find the simple interest earned after $2$ years on $\text{\$8,950}$ at an interest rate of $\text{3.24\%}.$

Solution

$579.96

Try it.

Find the simple interest earned after $3$ years on $\text{\$6,510}$ at an interest rate of $\text{2.85\%}.$

Try it.

Find the simple interest earned after $8$ years on $\text{\$15,500}$ at an interest rate of $\text{11.425\%}.$

Solution

$14,167

Try it.

Find the simple interest earned after $6$ years on $\text{\$23,900}$ at an interest rate of $\text{12.175\%}.$

Try it.

Find the principal invested if $\text{\$656}$ interest was earned in $5$ years at an interest rate of $\text{4\%}.$

Solution

$3,280

Try it.

Find the principal invested if $\text{\$177}$ interest was earned in $2$ years at an interest rate of $\text{3\%}.$

Try it.

Find the principal invested if $\text{\$70.95}$ interest was earned in $3$ years at an interest rate of $\text{2.75\%.}$

Solution

$860

Try it.

Find the principal invested if $\text{\$636.84}$ interest was earned in $6$ years at an interest rate of $\text{4.35\%.}$

Try it.

Find the principal invested if $\text{\$15,222.57}$ interest was earned in $6$ years at an interest rate of $\text{10.28\%}.$

Solution

$24,679.91

Try it.

Find the principal invested if $\text{\$10,953.70}$ interest was earned in $5$ years at an interest rate of $\text{11.04\%.}$

Try it.

Find the rate if a principal of $\text{\$5,400}$ earned $\text{\$432}$ interest in $2$ years.

Solution

Try it.

Find the rate if a principal of $\text{\$2,600}$ earned $\text{\$468}$ interest in $6$ years.

Try it.

Find the rate if a principal of $\text{\$11,000}$ earned $\text{\$1,815}$ interest in $3$ years.

Solution

5.5%

Try it.

Find the rate if a principal of $\text{\$8,500}$ earned $\text{\$3,230}$ interest in $4$ years.

Solve Simple Interest Applications

In the following exercises, solve the problem using the simple interest formula.

Try it.

Casey deposited $\text{\$1,450}$ in a bank account with interest rate $\text{4\%.}$ How much interest was earned in $2$ years?

Solution

$116

Try it.

Terrence deposited $\text{\$5,720}$ in a bank account with interest rate $\text{6\%.}$ How much interest was earned in $4$ years?

Try it.

Robin deposited $\text{\$31,000}$ in a bank account with interest rate $\text{5.2\%}.$ How much interest was earned in $3$ years?

Solution

$4,836

Try it.

Carleen deposited $\text{\$16,400}$ in a bank account with interest rate $\text{3.9\%}.$ How much interest was earned in $8$ years?

Try it.

Hilaria borrowed $\text{\$8,000}$ from her grandfather to pay for college. Five years later, she paid him back the $\text{\$8,000},$ plus $\text{\$1,200}$ interest. What was the rate of interest?

Solution

Try it.

Kenneth lent his niece $\text{\$1,200}$ to buy a computer. Two years later, she paid him back the $\text{\$1,200},$ plus $\text{\$96}$ interest. What was the rate of interest?

Try it.

Lebron lent his daughter $\text{\$20,000}$ to help her buy a condominium. When she sold the condominium four years later, she paid him the $\text{\$20,000},$ plus $\text{\$3,000}$ interest. What was the rate of interest?

Solution

3.75%

Try it.

Pablo borrowed $\text{\$50,000}$ to start a business. Three years later, he repaid the $\text{\$50,000},$ plus $\text{\$9,375}$ interest. What was the rate of interest?

Try it.

In $10$ years, a bank account that paid $\text{5.25\%}$ earned $\text{\$18,375}$ interest. What was the principal of the account?

Solution

$35,000

Try it.

In $25$ years, a bond that paid $\text{4.75\%}$ earned $\text{\$2,375}$ interest. What was the principal of the bond?

Try it.

Joshua's computer loan statement said he would pay $\text{\$1,244.34}$ in interest for a $3$ year loan at $\text{12.4\%}.$ How much did Joshua borrow to buy the computer?

Solution

$3,345

Try it.

Margaret's car loan statement said she would pay $\text{\$7,683.20}$ in interest for a $5$ year loan at $\text{9.8\%.}$ How much did Margaret borrow to buy the car?

Try it.

Caitlin invested $\text{\$8,200}$ in an $\text{18-month}$ certificate of deposit paying $\text{2.7\%}$ interest. How much interest did she earn form this investment?

Solution

$332.10

Try it.

Diego invested $\text{\$6,100}$ in a $\text{9-month}$ certificate of deposit paying $\text{1.8\%}$ interest. How much interest did he earn form this investment?

Try it.

Airin borrowed $\text{\$3,900}$ from her parents for the down payment on a car and promised to pay them back in $15$ months at a $\text{4\%}$ rate of interest. How much interest did she owe her parents?

Solution

$195.00

Try it.

Yuta borrowed $\text{\$840}$ from his brother to pay for his textbooks and promised to pay him back in $5$ months at a $\text{6\%}$ rate of interest. How much interest did Yuta owe his brother?

Condensed — the full section is in OpenStax Prealgebra 2e.

Practice (40)

Try each one on paper first. Reveal the answer to check; verified ones can be opened in the solver for every step.

Solve $0.6y=45.$
If you missed this problem, review .

အဖြေကို ဖော်ပြပါ

$75$
Solve $\frac{n}{1.45}=4.6.$
If you missed this problem, review .

အဖြေကို ဖော်ပြပါ

$6.67$

Find the simple interest earned after $3$ years on $\text{\$500}$ at an interest rate of $\text{6\%.}$

အဖြေကို ဖော်ပြပါ

Organize the given information in a list.

$\begin{array}{lll}I & = & ? \\ P & = & \text{\$500} \\ r & = & \text{6\%} \\ t & = & \text{3 years}\end{array}$

We will use the simple interest formula to find the interest.

Write the formula.	$I=Prt$
Substitute the given information. Remember to write the percent in decimal form.	$I=(500)(0.06)(3)$
Simplify.	$I=90$
Check your answer. Is $90 a reasonable interest earned on $500 in 3 years?
In 3 years the money earned 18%. If we rounded to 20%, the interest would have been 500(0.20) or $100. Yes, $90 is reasonable.
Write a complete sentence that answers the question.	The simple interest is $90.

Find the simple interest earned after $4$ years on $\text{\$800}$ at an interest rate of $\text{5\%.}$

အဖြေကို ဖော်ပြပါ

$160
Find the simple interest earned after $2$ years on $\text{\$700}$ at an interest rate of $\text{4\%.}$

အဖြေကို ဖော်ပြပါ

$56

Find the principal invested if $\text{\$178}$ interest was earned in $2$ years at an interest rate of $\text{4\%.}$

အဖြေကို ဖော်ပြပါ

Organize the given information in a list.

$\begin{array}{lll}I & = & \text{\$178} \\ P & = & ? \\ r & = & \text{4\%} \\ t & = & \text{2 years}\end{array}$

We will use the simple interest formula to find the principal.

Write the formula.	$I=Prt$
Substitute the given information.	$178=P(0.04)(2)$
Divide.	$\frac{178}{0.08}=\frac{0.08P}{0.08}$
Simplify.	$2,225=P$
Check your answer. Is it reasonable that $2,225 would earn $178 in 2 years?
$I=Prt$
$178\overset{?}{=}2,225(0.04)(2)$
$178=178✓$
Write a complete sentence that answers the question.	The principal is $2,225.

Find the principal invested if $\text{\$495}$ interest was earned in $3$ years at an interest rate of $\text{6\%.}$

အဖြေကို ဖော်ပြပါ

$2,750
Find the principal invested if $\text{\$1,246}$ interest was earned in $5$ years at an interest rate of $\text{7\%}.$

အဖြေကို ဖော်ပြပါ

$3,560

Find the rate if a principal of $\text{\$8,200}$ earned $\text{\$3,772}$ interest in $4$ years.

အဖြေကို ဖော်ပြပါ

Organize the given information.

$\begin{array}{lll}I & = & \text{\$3,772} \\ P & = & \text{\$8,200} \\ r & = & ? \\ t & = & \text{4 years}\end{array}$

We will use the simple interest formula to find the rate.

Write the formula.	$I=Prt$
Substitute the given information.	$3,772=8,200r(4)$
Multiply.	$3,772=32,800r$
Divide.	$\frac{3,772}{32,800}=\frac{32,800r}{32,800}$
Simplify.	$0.115=r$
Write as a percent.	$\text{11.5\%}=r$
Check your answer. Is 11.5% a reasonable rate if $3,772 was earned in 4 years?
$I=Prt$
$3,772\overset{?}{=}8,200(0.115)(4)$
$3,772=3,772✓$
Write a complete sentence that answers the question.	The rate was 11.5%.

Find the rate if a principal of $\text{\$5,000}$ earned $\text{\$1,350}$ interest in $6$ years.

အဖြေကို ဖော်ပြပါ

4.5%
Find the rate if a principal of $\text{\$9,000}$ earned $\text{\$1,755}$ interest in $3$ years.

အဖြေကို ဖော်ပြပါ

6.5%

Nathaly deposited $\text{\$12,500}$ in her bank account where it will earn $\text{4\%}$ interest. How much interest will Nathaly earn in $5$ years?

အဖြေကို ဖော်ပြပါ

We are asked to find the Interest, $I.$

Organize the given information in a list.

$\begin{array}{lll}I & = & ? \\ P & = & \text{\$12,500} \\ r & = & \text{4\%} \\ t & = & \text{5 years}\end{array}$

Write the formula.	$I=Prt$
Substitute the given information.	$I=(12,500)(0.04)(5)$
Simplify.	$I=2,500$
Check your answer. Is $2,500 a reasonable interest on $12,500 over 5 years?
At 4% interest per year, in 5 years the interest would be 20% of the principal. Is 20% of $12,500 equal to $2,500? Yes.
Write a complete sentence that answers the question.	The interest is $2,500.

Areli invested a principal of $\text{\$950}$ in her bank account with interest rate $\text{3\%.}$ How much interest did she earn in $5$ years?

အဖြေကို ဖော်ပြပါ

$142.50
Susana invested a principal of $\text{\$36,000}$ in her bank account with interest rate $\text{6.5\%}.$ How much interest did she earn in $3$ years?

အဖြေကို ဖော်ပြပါ

$7,020

အဖြေကို ဖော်ပြပါ

We are asked to find the rate of interest, $r.$

Organize the given information.

$\begin{array}{lll}I & = & 660 \\ P & = & \text{\$3,000} \\ r & = & ? \\ t & = & \text{4 years}\end{array}$

Write the formula.	$I=Prt$
Substitute the given information.	$660=(3,000)r(4)$
Multiply.	$660=(12,000)r$
Divide.	$\frac{660}{12,000}=\frac{(12,000)r}{12,000}$
Simplify.	$0.055=r$
Change to percent form.	$\text{5.5\%}=r$
Check your answer. Is 5.5% a reasonable interest rate to pay your brother?
$I=Prt$
$660\overset{?}{=}(3,000)(0.055)(4)$
$660=660✓$
Write a complete sentence that answers the question.	The rate of interest was 5.5%.

Jim lent his sister $\text{\$5,000}$ to help her buy a house. In $3$ years, she paid him the $\text{\$5,000},$ plus $\text{\$900}$ interest. What was the rate of interest?

အဖြေကို ဖော်ပြပါ

6%
Hang borrowed $\text{\$7,500}$ from her parents to pay her tuition. In $5$ years, she paid them $\text{\$1,500}$ interest in addition to the $\text{\$7,500}$ she borrowed. What was the rate of interest?

အဖြေကို ဖော်ပြပါ

4%

Eduardo noticed that his new car loan papers stated that with an interest rate of $\text{7.5\%},$ he would pay $\text{\$6,596.25}$ in interest over $5$ years. How much did he borrow to pay for his car?

အဖြေကို ဖော်ပြပါ

We are asked to find the principal, $P.$

Organize the given information.

$\begin{array}{lll}I & = & 6,596.25 \\ P & = & ? \\ r & = & \text{7.5\%} \\ t & = & \text{5 years}\end{array}$

Write the formula.	$I=Prt$
Substitute the given information.	$6,596.25=P(0.075)(5)$
Multiply.	$6,596.25=0.375P$
Divide.	$\frac{6,596.25}{0.375}=\frac{0.375P}{0.375}$
Simplify.	$17,590=P$
Check your answer. Is $17,590 a reasonable amount to borrow to buy a car?
$I=Prt$
$6,596.25\overset{?}{=}(17,590)(0.075)(5)$
$6,596.25=6,596.25✓$
Write a complete sentence that answers the question.	The amount borrowed was $17,590.

Sean's new car loan statement said he would pay $\text{\$4,866.25}$ in interest from an interest rate of $\text{8.5\%}$ over $5$ years. How much did he borrow to buy his new car?

အဖြေကို ဖော်ပြပါ

$11,450
In $5$ years, Gloria's bank account earned $\text{\$2,400}$ interest at $\text{5\%.}$ How much had she deposited in the account?

အဖြေကို ဖော်ပြပါ

$9,600

Caroline got $\text{\$900}$ as graduation gifts and invested it in a $\text{10-month}$ certificate of deposit that earned $\text{2.1\%}$ interest. How much interest did this investment earn?

အဖြေကို ဖော်ပြပါ

We are asked to find the interest, $I.$

Organize the given information.

$\begin{array}{lll}I & = & ? \\ P & = & \text{\$900} \\ r & = & \text{2.1\%} \\ t & = & \text{10 months}\end{array}$

Write the formula.	$I=Prt$
Substitute the given information, converting 10 months to $\frac{10}{12}$ of a year.	$I=\$900(0.021)(\frac{10}{12})$
Multiply.	$I=15.75$
Check your answer. Is $15.75 a reasonable amount of interest?
If Caroline had invested the $900 for a full year at 2% interest, the amount of interest would have been $18. Yes, $15.75 is reasonable.
Write a complete sentence that answers the question.	The interest earned was $15.75.

Adriana invested $\text{\$4,500}$ for $8$ months in an account that paid $\text{1.9\%}$ interest. How much interest did she earn?

အဖြေကို ဖော်ပြပါ

$57.00
Milton invested $\text{\$2,460}$ for $20$ months in an account that paid $\text{3.5\%}$ interest How much interest did he earn?

အဖြေကို ဖော်ပြပါ

$143.50
Interest Principal Rate Time (years)
$\text{\$1200}$ $\text{3\%}$ $5$

အဖြေကို ဖော်ပြပါ

$180
Interest Principal Rate Time (years)
$\text{\$1500}$ $\text{2\%}$ $\text{4}$
Interest Principal Rate Time (years)
$\$4410$ $\text{4.5\%}$ $\text{7}$

အဖြေကို ဖော်ပြပါ

$14,000
Interest Principal Rate Time (years)
$\$2112$ $\text{3.2\%}$ $\text{6}$
Interest Principal Rate Time (years)
$\$577.08$ $\text{\$4580}$ $\text{2}$

အဖြေကို ဖော်ပြပါ

6.3%
Interest Principal Rate Time (years)
$\$528.12$ $\text{\$3260}$ $\text{3}$
Find the simple interest earned after $5$ years on $\text{\$600}$ at an interest rate of $\text{3\%.}$

အဖြေကို ဖော်ပြပါ

$90
Find the simple interest earned after $4$ years on $\text{\$900}$ at an interest rate of $\text{6\%.}$
Find the simple interest earned after $2$ years on $\text{\$8,950}$ at an interest rate of $\text{3.24\%}.$

အဖြေကို ဖော်ပြပါ

$579.96
Find the simple interest earned after $3$ years on $\text{\$6,510}$ at an interest rate of $\text{2.85\%}.$
Find the simple interest earned after $8$ years on $\text{\$15,500}$ at an interest rate of $\text{11.425\%}.$

အဖြေကို ဖော်ပြပါ

$14,167
Find the simple interest earned after $6$ years on $\text{\$23,900}$ at an interest rate of $\text{12.175\%}.$
Find the principal invested if $\text{\$656}$ interest was earned in $5$ years at an interest rate of $\text{4\%}.$

အဖြေကို ဖော်ပြပါ

$3,280
Find the principal invested if $\text{\$177}$ interest was earned in $2$ years at an interest rate of $\text{3\%}.$
Find the principal invested if $\text{\$70.95}$ interest was earned in $3$ years at an interest rate of $\text{2.75\%.}$

အဖြေကို ဖော်ပြပါ

$860
Find the principal invested if $\text{\$636.84}$ interest was earned in $6$ years at an interest rate of $\text{4.35\%.}$
Find the principal invested if $\text{\$15,222.57}$ interest was earned in $6$ years at an interest rate of $\text{10.28\%}.$

အဖြေကို ဖော်ပြပါ

$24,679.91

Symbols used here

\pm

plus or minus
Both signs at once: x = 3 ± 2 means 5 and 1.

\neq

not equal
The two sides are different.

\leq,\ \geq

less/greater than or equal
Inequalities that allow equality; < and > exclude it.

\approx

approximately equal
Equal to the precision shown, not exactly.

\sqrt{x},\ \sqrt[n]{x}

square root, n-th root
The non-negative number whose square (n-th power) is x.

a \bmod n

remainder
What is left after dividing a by n.

per cent
Per hundred: 15% = 15/100.

a : b,\ \frac{a}{b}

ratio, fraction
a for every b; a divided by b.

How to: Solve Simple Interest Applications

Use the simple interest formula
Solve simple interest applications
If an amount of money,
Interest earned according to this formula is called

Questions people ask

Why does the order of operations matter?

Because 2 + 3 × 4 would otherwise be two different numbers. The convention (brackets, exponents, multiplication and division, addition and subtraction) exists so every reader gets the same value from the same expression.

How do I check an arithmetic answer?

Estimate first (round every number and compute roughly), then compare. If the estimate and the exact answer disagree by more than a little, one of them is wrong. The solver shows every operation, so you can find which line went astray.

Why are fractions harder than decimals?

They are not harder, they are more exact: 1/3 is a precise number, 0.333 is an approximation. Fractions need a common denominator to add, which is the one extra step people trip on.

သင့်ရဲ့ကိုယ်ပိုင်စမ်းသပ်

Parts of this page are adapted from OpenStax Prealgebra 2e (CC BY-NC-SA 4.0). Condensed and re-explained here; errors are ours.

ပိုပြီး Arithmetic

Order of operations Fractions Percentages Powers and roots

Write the formula.	\(I=Prt\)
Substitute the given information. Remember to write the percent in decimal form.	\(I=(500)(0.06)(3)\)
Simplify.	\(I=90\)
Check your answer. Is $90 a reasonable interest earned on $500 in 3 years?
In 3 years the money earned 18%. If we rounded to 20%, the interest would have been 500(0.20) or $100. Yes, $90 is reasonable.
Write a complete sentence that answers the question.	The simple interest is $90.