Simple Interest Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

A hospital administrator places $\$12,000$ into a fixed-term savings certificate that earns an annual simple interest rate of $4.2\%$ . If no other deposits or withdrawals are made, what is the total accumulated balance, in dollars, of the certificate after exactly 30 months?

Show answer & explanation

Answer: 13260

Answer

The total accumulated balance is 13260.

The correct answer is found by first converting the 30-month time period into 2.5 years (

30 \div 12 = 2.5

), and the

4.2\%

interest rate into the decimal

0.042

(

4.2 \div 100 = 0.042

). Using the simple interest formula

I = P \times R \times T

, the interest earned is

\$12,000 \times 0.042 \times 2.5 = \$1,260

. Adding this interest to the original principal of

\$12,000

gives a total accumulated balance of

\$13,260

.

Step-by-Step Solution

1

Convert the interest rate to a decimal and the time period to years.

R = 4.2\% = 0.042

, and

T = 30 \text{ months} \div 12 \text{ months/year} = 2.5 \text{ years}

.

The standard simple interest formula requires the interest rate as a decimal and the time expressed in years.

2

Calculate the total interest earned using the simple interest formula

I = P \times R \times T

.

I = 12000 \times 0.042 \times 2.5 = 1260

This determines how much additional money the certificate earns over the 30-month period.

3

Calculate the total accumulated balance by adding the interest earned to the original principal.

Total Balance =

12000 + 1260 = 13260

The question asks for the total accumulated balance, which includes both the initial deposit (principal) and the earned interest.

Key Concept

Calculating simple interest over a fractional year and determining the total accumulated amount.

Question 2Question →

A civil engineer needs to earn exactly $\$840$ in simple interest over a $10$ -month period to offset the cost of new drafting software. If a local credit union offers a business savings account with a $4.8\%$ annual simple interest rate, how much principal must be deposited into the account?

\$1,750

\$2,100

\$17,500

\$21,000

Show answer & explanation

Answer: $\$21,000$

Answer

The correct principal amount to deposit is

\$21,000

.

The correct answer accurately uses the simple interest formula by first converting the 10-month period into a fraction of a year (

10/12

or

5/6

). Multiplying the annual rate of

0.048

by

5/6

yields

0.04

. Dividing the target interest of

\$840

by

0.04

correctly determines the required principal.

Step-by-Step Solution

1

Identify the known variables from the problem.

Interest (

I

) =

\$840

, annual rate (

r

) =

4.8\% = 0.048

, and time (

t

) =

10

months.

Organizing the given information clarifies what is needed for the simple interest formula.

2

Convert the time period from months to years because the interest rate is an annual rate.

t = \frac{10}{12} = \frac{5}{6} \text{ years}

Standard simple interest formulas require time to be in the same unit as the rate.

3

Substitute the values into the simple interest formula

I = P \times r \times t

to set up the equation.

840 = P \times 0.048 \times \frac{5}{6}

This establishes the mathematical relationship to isolate the unknown principal amount (

P

).

4

Simplify the equation and solve for the principal.

840 = P \times 0.04 \Rightarrow P = \frac{840}{0.04} = 21000

Dividing both sides by the calculated coefficient isolates

P

and yields the final answer.

Key Concept

Solving for Principal using the Simple Interest Formula

Question 3Question →

A small business owner takes out a $\$12,500$ personal loan to finance new equipment. The loan agreement specifies an annual simple interest rate of $6.4\%$ . If the owner repays the loan in full at the end of $45$ months, what is the total amount that must be repaid?

\$12,800

\$13,300

\$15,500

\$16,100

Show answer & explanation

Answer: $\$15,500$

Answer

\$15,500

The correct total amount to repay is found by first converting the 45-month term into years by dividing by 12, which gives 3.75 years. Next, the simple interest is calculated by multiplying the principal (

\$12,500

), the annual rate as a decimal (

0.064

), and the time in years (

3.75

) to get

\$3,000

. Finally, adding this interest to the original principal yields the total repayment amount of

\$15,500

.

Step-by-Step Solution

1

Convert the loan duration from months to years.

45 \text{ months} \div 12 \text{ months/year} = 3.75 \text{ years}

The interest rate is an annual rate, so the time period in the formula must be expressed in years.

2

Calculate the total simple interest earned over the period.

I = P \times r \times t = \$12,500 \times 0.064 \times 3.75 = \$3,000

This determines the additional cost of borrowing the money for the specified time.

3

Add the calculated interest to the original principal to find the total repayment amount.

A = \$12,500 + \$3,000 = \$15,500

The question asks for the total amount that must be repaid, which includes both the principal balance and the accumulated interest.

Key Concept

To find the total amount to be repaid on a loan, you must calculate the simple interest using the formula

I = P \times r \times t

, ensuring the time

t

is converted to years, and then add this interest to the principal

P

.

Question 4Question →

A developer issues a short-term promissory note to cover construction costs. The note carries an annual simple interest rate of $8\%$ . After $9$ months, the developer repays a total of $\$42,400$ , which includes both the original principal borrowed and the interest earned. What was the original principal amount borrowed, in dollars?

Show answer & explanation

Answer: 40000

Answer

40000

The original principal is found by utilizing the total amount formula for simple interest,

A = P(1 + rt)

, and solving for

P

. By substituting

A = 42,400

,

r = 0.08

, and

t = 0.75

years (from

9

months), the equation simplifies to

1.06P = 42,400

, which yields a principal of $40,000.

Step-by-Step Solution

1

Identify the known variables from the word problem.

Total Amount (

A

) =

42,400

, Rate (

r

) =

8\% = 0.08

, Time (

t

) =

9

months.

Extracting the specific numbers and their corresponding variables is required before applying any formulas.

2

Convert the time duration from months into years.

t = \frac{9}{12} = 0.75

years.

Simple interest formulas require the time unit to match the rate unit, which is annual (

8\%

per year).

3

Apply the total amount simple interest formula and substitute the values.

42,400 = P(1 + 0.08 \times 0.75)

The total amount paid back (

42,400

) includes both the principal (

P

) and the interest (

Prt

), factored out as

P(1 + rt)

.

4

Simplify the equation.

42,400 = P(1 + 0.06) \Rightarrow 42,400 = 1.06P

Multiplying the rate by the time yields the total interest multiplier (

6\%

or

0.06

), adding it to

1

gives the total amount multiplier.

5

Solve for the principal (

P

).

P = \frac{42,400}{1.06} = 40,000

Isolating

P

gives the original amount borrowed. The division can be calculated mentally by noting that

424

is

4 \times 106

.

Key Concept

Solving for Principal in a Simple Interest Total Amount Scenario

Question 5Question →

A mechanic takes out a $\$3,000$ loan to purchase upgraded tools. The loan agreement includes a $4\%$ annual simple interest rate. If the loan is paid off in exactly $3$ years, what is the total amount of interest paid?

Show answer & explanation

Answer: 360

Answer

360

The simple interest formula is

I = P \times R \times T

. By plugging in the principal (

\$3,000

), the decimal interest rate (

0.04

), and the time (

3

years), the calculation is

3000 \times 0.04 \times 3 = 360

. Therefore, the total interest paid is

\$360

.

Step-by-Step Solution

1

Identify the given values from the problem statement.

P = 3000

,

R = 4\%

,

T = 3

years

These are the required variables for the simple interest formula.

2

Convert the percentage rate to a decimal.

R = 0.04

Percentages must be in decimal form to perform calculations.

3

Apply the simple interest formula

I = P \times R \times T

.

I = 3000 \times 0.04 \times 3

This formula calculates the total interest earned or paid over a specific time period.

4

Calculate the final product.

360

Multiplying the principal by the rate gives the interest for one year (

120

), and multiplying by 3 gives the total for three years.

Key Concept

Calculating simple interest over a multi-year period.

Question 6Question →

A homeowner finances a new refrigerator using a $\$1,200$ store credit plan. The plan charges an annual simple interest rate of $5\%$ . If the homeowner pays off the balance in exactly $2$ years without any prior payments, what is the total amount of interest paid, in dollars?

Show answer & explanation

Answer: 120

Answer

120

The total interest is found by multiplying the principal amount by the annual interest rate and the time in years. Using the formula

I = P \times R \times T

, the calculation is

1200 \times 0.05 \times 2

, which equals $120.

Step-by-Step Solution

1

Identify the given values for principal, rate, and time.

Principal

P = 1200

, Rate

R = 5\% = 0.05

, Time

T = 2

years.

These are the necessary variables for the simple interest formula.

2

Apply the simple interest formula.

I = 1200 \times 0.05 \times 2

The formula for simple interest is

I = P \times R \times T

.

3

Calculate the final product.

I = 120

Multiplying the values determines the total interest paid over the

2

-year period.

Key Concept

Calculating simple interest using the formula

I = P \times R \times T

Question 7Question →

A customer deposits $\$3,000$ into a savings account that pays an annual simple interest rate of $6\%$ . If no additional deposits or withdrawals are made, how much total interest will the account earn after $2$ years?

\$36

\$180

\$360

\$3,600

Show answer & explanation

Answer: \$360

Answer

The account will earn

\$360

in total interest.

The formula for simple interest is

I = P \times R \times T

, where

P

is the principal,

R

is the annual interest rate as a decimal, and

T

is the time in years. Substituting the given values:

I = \$3,000 \times 0.06 \times 2 = \$360

.

Step-by-Step Solution

1

Identify the given values for principal, rate, and time.

P = \$3,000

,

R = 6\% = 0.06

,

T = 2

years.

These are the necessary components for the simple interest formula.

2

Apply the simple interest formula

I = P \times R \times T

.

I = \$3,000 \times 0.06 \times 2

This formula calculates the total interest earned over the given time period.

3

Multiply the values to find the total interest.

I = \$360

This provides the final amount of interest earned.

Key Concept

Simple Interest

Question 8Question →

An individual borrows $\$4,000$ to purchase a used motorcycle. The loan has an annual simple interest rate of $7\%$ . If the loan is paid off in exactly $24$ months, how much total interest will the borrower pay?

\$280

\$560

\$5,600

\$6,720

Show answer & explanation

Answer: $\$560$

Answer

The total interest paid is

\$560

.

The correct answer accurately uses the simple interest formula

I = P \times R \times T

. The principal (

P

) is

\$4,000

, the rate (

R

) is

0.07

, and the time (

T

) in years is

2

(since

24

months equals

2

years). Multiplying these together yields

\$4,000 \times 0.07 \times 2 = \$560

.

Step-by-Step Solution

1

Identify the principal amount (

P

), annual interest rate (

R

), and time (

T

) given in the problem.

P = \$4,000

,

R = 7\%

, and

T = 24

months.

These are the required variables for the simple interest formula.

2

Convert the interest rate from a percentage to a decimal.

7\% = 0.07

Mathematical formulas require percentages to be in decimal form.

3

Convert the time duration from months to years to match the annual interest rate.

24 \text{ months} \div 12 \text{ months/year} = 2 \text{ years}

.

The interest rate is annual, so the time must also be in years.

4

Apply the simple interest formula,

I = P \times R \times T

.

I = \$4,000 \times 0.07 \times 2 = \$560

.

This calculates the total interest accrued over the 2-year period.

Key Concept

Simple Interest Calculation with Time Conversion

Question 9Question →

A graphic designer places $\$8,000$ into a high-yield savings certificate that pays an annual simple interest rate of $4.5\%$ . Upon maturity, the account has generated exactly $\$270$ in interest. How many months was the money invested?

0.75

7.5

9

12

Show answer & explanation

Answer: 9

Answer

The money was invested for exactly 9 months.

The investment earns

\$360

in a full year (

\$8,000 \times 0.045 = \$360

). Since the actual interest earned is

\$270

, the time in years is

270 / 360

, which simplifies to

3/4

or

0.75

years. Multiplying

0.75

years by

12

months per year gives exactly

9

months.

Step-by-Step Solution

1

Identify the given variables and the simple interest formula.

Principal (

P

) =

\$8,000

, Interest (

I

) =

\$270

, Rate (

r

) =

4.5\%

or

0.045

. The formula is

I = P \times r \times t

.

Setting up the standard formula is the first step to isolate and find the unknown time variable.

2

Calculate the amount of interest earned in one full year.

\$8,000 \times 0.045 = \$360

per year.

Finding the annual interest provides the denominator needed to determine what fraction of a year the money was invested.

3

Divide the actual interest earned by the annual interest to find the time in years.

\$270 / \$360 = 0.75

years.

The ratio of earned interest to annual interest gives the exact time the money remained in the account in years.

4

Convert the time from years into months.

0.75 \text{ years} \times 12 \text{ months/year} = 9 \text{ months}

.

The question specifically asks for the time duration in months, requiring a final unit conversion.

Key Concept

Calculating the time duration of an investment using the simple interest formula and converting the resulting fractional year into months.

Estimated Time:1m 30s

Question 10Question →

A retiree wants to earn exactly $1,800$ in simple interest over a period of 15 months to help pay for a vacation. A local credit union offers a short-term investment account with an annual simple interest rate of $4\%$ . Assuming no other deposits or withdrawals are made, how much money must the retiree deposit initially to reach this interest goal?

$3,000

$3,600

$36,000

$45,000

Show answer & explanation

Answer: $36,000

Answer

$36,000

To find the initial deposit (principal), the simple interest formula

I = P \times R \times T

must be rearranged to solve for

P

, yielding

P = \frac{I}{R \times T}

. Because the rate is an annual percentage, the 15-month period must first be converted into years (

15 / 12 = 1.25

years). Substituting the given values gives

P = \frac{1800}{0.04 \times 1.25}

, which simplifies to

1800 / 0.05 = 36000

. Therefore, an initial deposit of

36,000

is required.

Step-by-Step Solution

1

Convert the time duration from months to years.

T = \frac{15}{12} = 1.25

years

The interest rate is provided as an annual rate, so the time factor in the simple interest formula must also be expressed in years.

2

Set up the simple interest formula with the known values.

I = P \times R \times T \rightarrow 1800 = P \times 0.04 \times 1.25

The formula connects the interest earned (

I

) to the principal (

P

), rate (

R

), and time (

T

).

3

Solve for the unknown principal (

P

).

P = \frac{1800}{0.04 \times 1.25} = \frac{1800}{0.05} = 36000

Isolating

P

determines the initial deposit required to reach the interest goal.

Key Concept

Calculating the initial principal using the simple interest formula by isolating the principal variable and properly converting time into years.

Question 11Question →

A college student invests $\$2,500$ of their scholarship money into a bank savings certificate that pays an annual simple interest rate of $3.6\%$ . How many months will it take for the investment to earn exactly $\$135$ in interest?

Show answer & explanation

Answer: 18

Answer

18

The simple interest formula is

I = P \times r \times t

. Substituting the given values gives

135 = 2500 \times 0.036 \times t

. Solving for

t

yields

1.5

years. Multiplying by 12 converts this to exactly 18 months.

Step-by-Step Solution

1

Identify the simple interest formula and the given values.

I = P \times r \times t

, where

I = \$135

,

P = \$2,500

, and

r = 0.036

.

To set up the equation to solve for the unknown time variable.

2

Substitute the values into the formula and simplify.

135 = 2500 \times 0.036 \times t

, which simplifies to

135 = 90t

.

To isolate the term with the unknown variable.

3

Solve for the time

t

in years.

t = 135 / 90 = 1.5

years.

The standard simple interest formula calculates time in years.

4

Convert the time from years to months.

1.5 \times 12 = 18

months.

The question specifically asks for the duration in months.

Key Concept

Simple Interest

Question 12Question →

A small business owner takes out a loan of $\$15,000$ to repair commercial equipment. After exactly 8 months, the loan is paid off with a single payment of $\$15,900$ . Assuming simple interest is applied, what is the annual interest rate on the loan?

6\%

9\%

4\%

7.5\%

Show answer & explanation

Answer: $9\%$

Answer

The annual simple interest rate on the loan is

9\%

.

To find the annual interest rate, we first determine the total interest paid by subtracting the principal from the total payment (

\$15,900 - \$15,000 = \$900

). Next, we convert the 8-month term into years by dividing by 12, which gives

2/3

of a year. Plugging these into the simple interest formula,

I = P \times R \times T

, gives

900 = 15,000 \times R \times (2/3)

. Simplifying the right side yields

900 = 10,000 \times R

. Dividing both sides by 10,000 results in

R = 0.09

, or

9\%

.

Step-by-Step Solution

1

Calculate the total amount of interest paid.

\$15,900 - \$15,000 = \$900

The simple interest formula requires the interest amount, which is the difference between the total payoff amount and the original principal.

2

Convert the loan duration from months into a fraction of a year.

8 \text{ months} = \frac{8}{12} \text{ year} = \frac{2}{3} \text{ year}

Annual simple interest rates require the time variable (

T

) to be expressed in years.

3

Substitute the known values into the simple interest formula (

I = P \times R \times T

) and solve for the rate (

R

).

\$900 = \$15,000 \times R \times \frac{2}{3}

\$900 = \$10,000 \times R

R = \frac{900}{10,000} = 0.09 = 9\%

Isolating

R

provides the annual interest rate in decimal form, which is then converted to a percentage.

Key Concept

Calculating the annual simple interest rate when given the principal, the total maturity amount, and a fractional time period in months.

Question 13Question →

To fund a certification course, a network administrator invested a specific amount of money into a standard savings account yielding $5\%$ annual simple interest. After leaving the funds untouched for $30$ months, the investment generated exactly $\$375$ in interest alone. What was the initial amount deposited into the account?

Show answer & explanation

Answer: 3000

Answer

The initial amount deposited was $3,000.

The principal is found by dividing the interest earned by the product of the annual interest rate and the time in years. Converting

30

months to

2.5

years and using the

5\%

rate as

0.05

, the calculation is

375 \div (0.05 \times 2.5) = 3000

.

Step-by-Step Solution

1

Identify the given variables for the simple interest formula.

I = 375

,

r = 0.05

,

t = 30

months.

The formula requires these values to solve for the unknown principal

P

.

2

Convert the time period from months to years.

t = \frac{30}{12} = 2.5

years.

The given interest rate is an annual rate, so the time must also be expressed in years.

3

Set up the simple interest equation.

375 = P \times 0.05 \times 2.5

Using the standard simple interest formula

I = P \times r \times t

.

4

Solve for the principal

P

.

P = \frac{375}{0.125} = 3000

Isolating

P

provides the final initial deposit amount.

Key Concept

Calculating the principal using the simple interest formula over a fractional year term.

Question 14Question →

An investor divides her $24,000 savings into two different accounts. She places a portion into a high-yield certificate earning 9% annual simple interest, and the remainder into a short-term bond earning 6% annual simple interest. After 18 months, the combined simple interest earned from both accounts is exactly$ 2,430. How much money was originally invested at the 9% rate?

$6,000

$18,000

$14,400

$600

Show answer & explanation

Answer: $6,000

Answer

The amount invested at the 9% rate is $6,000.

The correct answer is derived by modeling the split investment algebraically. By assigning

x

to the 9% investment, the 6% investment becomes

24,000 - x

. Applying the formula

I = Prt

with

t = 1.5

years to both parts yields

0.09(1.5)x + 0.06(1.5)(24,000 - x) = 2,430

. Simplifying this to

0.135x + 2,160 - 0.09x = 2,430

leaves

0.045x = 270

. Dividing 270 by 0.045 confirms that $6,000 was invested at 9%.

Step-by-Step Solution

1

Convert the investment duration from months to years.

18 months = 1.5 years.

The simple interest formula

I = Prt

requires time

t

to be expressed in years when dealing with annual interest rates.

2

Define variables for the two investment amounts.

Let

x

be the amount invested at 9%. The remaining amount invested at 6% is

(24,000 - x)

.

This allows us to represent both unknown principals in terms of a single variable, making the equation solvable.

3

Set up the total interest equation using

I = Prt

.

x(0.09)(1.5) + (24,000 - x)(0.06)(1.5) = 2,430

The sum of the simple interest earned from the 9% account and the 6% account must equal the total interest of $2,430.

4

Distribute and simplify the terms in the equation.

0.135x + (24,000 - x)(0.09) = 2,430 \Rightarrow 0.135x + 2,160 - 0.09x = 2,430

Multiplying the rate and time constants makes it easier to isolate

x

.

5

Combine like terms and solve for

x

.

0.045x = 270 \Rightarrow x = \frac{270}{0.045} = 6,000

Isolating

x

provides the original amount invested at the 9% rate.

Key Concept

Systems of Simple Interest

Estimated Time:3m 0s

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