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📝 Simple interest formula: Find interest earned (13 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 13 questions available

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What is Simple interest formula: Find interest earned?

Definition:
The simple interest formula is $I = P r t$ , where $I$ is interest earned, $P$ is the principal (initial amount), $r$ is the annual interest rate (as a decimal), and $t$ is time in years. To find interest, multiply principal by rate and time.

Working:
For example, if you invest \ $1000 at 5% annual interest for 3 years,$

2

Easy

4

Medium

7

Hard

📝 All Simple interest formula: Find interest earned MCQs

Q1. A student deposits \ $2,400 in an account earning simple interest at 5% per year for 3 years. How much interest will be earned?</p><div class="options-grid"><div class="opt-item "><span class="label">A.</span><span class="text">\$ 120

B.\$240

C.\$360 ✅

D.\$3,600

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: Using the simple-interest model $I=Prt$ , substitute $P=2400$ , $r=0.05$ , and $t=3$ . Thus $I=2400(0.05)(3)=360$ . The interest earned is therefore \$360, while the larger distractors confuse interest with the final amount.

Q2. An investment of \$1,800 earns simple interest at an annual rate of 4.5% for 2 years. Which expression correctly represents the interest earned?

A.

1800(4.5)(2)

B.

1800(0.045)(2)

✅

C.

1800(0.45)(2)

D.

1800(4.5)(0.02)

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The annual percentage rate must be converted from 4.5% to decimal form, giving $0.045$ . The time is already measured in years, so $I=1800(0.045)(2)$ . Using 4.5 directly would incorrectly make the interest 100 times too large.

Q3. Two accounts each receive \ $3,000. Account A earns 4% simple interest for 5 years, while Account B earns 5% simple interest for 4 years. Which statement is correct?</p><div class="options-grid"><div class="opt-item "><span class="label">A.</span><span class="text">Account A earns \$ 120 more

B.Account B earns \$120 more

C.Both accounts earn the same interest ✅

D.Account B earns twice as much

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: For Account A, $I=3000(0.04)(5)=600$ . For Account B, $I=3000(0.05)(4)=600$ . Although the rates and times differ, their products $rt$ are equal, so both investments earn exactly \$600 in interest.

Q4. A charity places \ $5,000 in a simple-interest account. After 18 months, it wants to know the interest earned at an annual rate of 6%. What is the interest?</p><div class="options-grid"><div class="opt-item "><span class="label">A.</span><span class="text">\$ 300

B.\$450 ✅

C.\$540

D.\$600

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The time must be expressed in years because the rate is annual. Eighteen months equals $18/12=1.5$ years. Therefore, $I=5000(0.06)(1.5)=450$ . Treating 18 as the time would ignore the required unit conversion.

Q5. A borrower invests \ $7,500 at 3.2% simple interest. The investment remains untouched for 30 months. How much interest accumulates?</p><div class="options-grid"><div class="opt-item "><span class="label">A.</span><span class="text">\$ 480

B.\$600 ✅

C.\$720

D.\$7,740

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Thirty months is $30/12=2.5$ years. Applying $I=Prt$ gives $I=7500(0.032)(2.5)=600$ . The answer \ $720 results from using 3 years, while \$ 7,740 represents the total amount rather than interest alone.

Q6. A savings account earns simple interest. A student claims that increasing the interest rate from 4% to 8% while keeping the principal and time unchanged will double the interest. Is the claim valid?

A.No, because interest is independent of the rate

B.No, because doubling the rate quadruples the interest

C.Yes, because interest is directly proportional to the rate ✅

D.Yes, but only when the principal is also doubled

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: With principal and time fixed, $I=Prt$ shows that interest is directly proportional to the rate. Therefore, doubling the rate from 4% to 8% doubles the interest. This conclusion follows from the structure of the model, not merely from calculation.

Q7. A student calculates the interest on \$4,000 at 5% for 2 years as $4000(5)(2)=40,000$ . What is the main error?

A.The principal should be divided by 100 twice

B.The percentage rate was not converted to decimal form ✅

C.The time should be measured in months

D.The principal should be converted to a percentage

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The rate $5\%$ must be written as $0.05$ before substitution. The correct calculation is $4000(0.05)(2)=400$ . Using 5 instead of 0.05 multiplies the result by 100, producing the unrealistic value of \$40,000.

Q8. A worker says that \ $6,000 invested at 7% for 3 years earns \$ 1,260 because $6000+6000(0.07)(3)=7260$ . Which statement best evaluates the reasoning?

A.The interest is \$7,260

B.The interest is \

1,260, but the final amount is \

7,260 ✅

C.The interest is \

1,260, but the final amount is \

6,000

D.The interest is \$420, because the rate applies only once

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The calculation $6000(0.07)(3)=1260$ correctly finds the interest. However, adding the principal produces the final amount, $6000+1260=7260$ . The mistake would be calling the total balance the interest earned.

Q9. A graph shows interest $I$ on the vertical axis and time $t$ in years on the horizontal axis. The line passes through $(0,0)$ and $(4,800)$ . If the principal and rate remain unchanged, what interest corresponds to 7 years?

A.\$1,000

B.\$1,200

C.\$1,400 ✅

D.\$1,600

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The graph represents a linear relationship because simple interest increases at a constant rate with time. From $(0,0)$ to $(4,800)$ , the slope is $800/4=200$ dollars per year. At 7 years, $I=200(7)=1400$ .

Q10. A person can choose between two investments. Investment A uses \ $4,500 at 6% simple interest for 2 years. Investment B uses \$ 5,000 at 5% simple interest for 2 years. Which choice earns more interest, and by how much?

A.A by \$40 ✅

B.A by \$100

C.B by \$40

D.B by \$100

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: Investment A earns $4500(0.06)(2)=540$ . Investment B earns $5000(0.05)(2)=500$ . Therefore, Investment A earns \$40 more. The comparison demonstrates why both principal and rate must be considered rather than choosing only the higher rate or principal.

Q11. A graph of simple interest against time has a straight line through $(0,0)$ . One investment has a steeper line than another, even though both start at zero. What does the steeper line indicate?

A.A smaller principal only

B.A lower combined rate and principal

C.A greater interest earned per unit of time ✅

D.A shorter investment period

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: For fixed principal and rate, the slope of an interest-versus-time graph represents $Pr$ , the amount of interest earned each year. A steeper line therefore indicates a larger annual interest accumulation, caused by a larger principal, rate, or both.

Q12. An investment earns \ $900 of simple interest from a principal of \$ 6,000 at 5% annually. Before solving for time, a student estimates that the investment must have lasted about 3 years. Which reasoning best verifies the estimate?

A.Because

6000(0.05)=300

dollars is earned each year,

900/300=3

years ✅

B.Because 5% of \

900 is \

45, the time is 20 years

C.Because \

6,000 divided by \

900 is approximately 6.7 years

D.Because the interest rate and interest amount are both percentages

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: The annual interest is $Pr=6000(0.05)=300$ dollars. To accumulate \$900, the required time is $900/300=3$ years. This approach checks the reasonableness of the result by interpreting the model as a constant yearly earning.

Q13. A student has \ $8,000 available and wants at least \$ 1,200 in simple interest over 3 years. What is the minimum annual interest rate required?

A.0.04

B.0.05 ✅

C.0.06

D.0.075

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Use $I=Prt$ and solve for the rate: $r=I/(Pt)=1200/(8000\cdot3)=0.05$ , which is 5%. Therefore, 5% is sufficient, while rates below it produce less than \$1,200. The correct answer is B.

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