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📝 Find principal using simple interest formula I=Prt (11 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 11 questions available

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What is Find principal using simple interest formula I=Prt?

Definition:
The principal is the original amount of money invested or borrowed before any interest is applied, and it can be found by rearranging the simple interest formula $I = Prt$ , where $I$ is the interest earned or paid, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years, allowing us to solve for $P$ by dividing the interest by the product of rate and time, so $P = \frac{I}{rt}$ .

Working:
To find the principal, we isolate $P$ in the equation by dividing both sides by $rt$ , giving $P = \frac{I}{rt}$ , and it is important to ensure that the rate is expressed as a decimal (e.g., 5% becomes 0.05) and the time is in years, with the units matching so that the principal is in the same currency as the interest.

Example:
If an investment earns $\240 \) in simple interest over 3 years at an annual rate of 4%, then $I = 240$ , $r = 0.04$ , $t = 3$ , so the principal is $P = \frac{240}{0.04 \times 3} = \frac{240}{0.12} = \2000$ , meaning you originally invested $\$2000$ .

Reason:
Finding the principal is essential in finance to determine the initial investment or loan amount needed to achieve a desired interest income, or to understand the base amount before interest accrues, which is crucial for budgeting, investment planning, and loan management.

Easy

Medium

Hard

📝 All Find principal using simple interest formula I=Prt MCQs

Q1. An investment earns $\$720$ in simple interest at an annual rate of $6\%$ for $4$ years. What was the original principal?

\$2,400

\$3,000

✅

\$3,600

\$4,800

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: Using $I=Prt$ , solve for the principal with $P=\frac{I}{rt}$ . Substituting $I=720$ , $r=0.06$ , and $t=4$ gives $P=\frac{720}{0.24}=\$3,000$ .

Q2. Two investments earn the same $\$900$ of simple interest over $5$ years. Investment A has a rate of $4\%$ , while Investment B has a rate of $6\%$ . Which comparison of their principals is correct?

A.Investment A has a larger principal by

50\%

B.Investment B has a larger principal by

50\%

C.Investment A has a principal

50\%

larger than Investment B. ✅

D.Both principals are equal.

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: Because the interest, rate, and time are related by $P=\frac{I}{rt}$ , principal varies inversely with the rate. Investment A requires $900/(0.04\cdot5)=\4,500 \), while B requires $\3,000$ , making A 50% larger.

Q3. A borrower paid $\1,200 \) in simple interest on a loan lasting $4$ years at $7.5\%$ annually. Before calculating, a student says the principal must be $\9,000$ because $1,200\div0.075$ equals $16,000$ . What is the correct principal?

\$3,000

\$4,000

✅

\$5,000

\$6,000

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The student's error is ignoring the four-year time factor. The correct calculation is $P=\frac{1,200}{0.075(4)}=\frac{1,200}{0.30}=\$4,000$ . Dividing only by the rate would incorrectly treat the loan as lasting one year.

Q4. A student needs $\2,400 \) after earning $\400$ in simple interest over $5$ years. If the annual rate is $r$ , which equation correctly models the situation for finding the principal?

2400=P(1+5r)

400=P(5r)

✅

400=P+5r

2400=Pr

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The given interest, rather than the final amount, is $\$400$ . Since simple interest satisfies $I=Prt$ , substituting $I=400$ and $t=5$ gives $400=P(5r)$ , which directly models the unknown principal.

Q5. A company borrows money at $8\%$ simple interest for $18$ months and pays $\$720$ in interest. What was the amount borrowed?

\$4,800

\$5,000

\$6,000

✅

\$7,200

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The time must be converted from months to years: $18$ months equals $1.5$ years. Then $P=\frac{720}{0.08(1.5)}=\frac{720}{0.12}=\$6,000$ . The conversion is essential because the rate is annual.

Q6. A community organization invests money at $5.5\%$ simple interest. After $2.5$ years, the interest earned is $\$825$ . What principal was invested?

\$4,500

\$5,000

\$5,500

\$6,000

✅

💡 Difficulty: medium | ✅ Correct: D

📖 Explanation: Apply $P=\frac{I}{rt}$ using $I=825$ , $r=0.055$ , and $t=2.5$ . This gives $P=\frac{825}{0.1375}=\$6,000$ , so option D is actually correct. The key challenge is accurately combining the decimal rate and fractional year.

Q7. A graph plots simple interest $I$ vertically against time $t$ horizontally for a fixed rate. The line passes through the point $(4,960)$ , meaning the interest after $4$ years is $\$960$ . If the rate is $6\%$ , what principal does the graph imply?

\$2,000

\$3,000

\$4,000

✅

\$6,000

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: At $t=4$ , the graph indicates $I=960$ . Using $I=Prt$ , the principal is $P=\frac{960}{0.06(4)}=\frac{960}{0.24}=\$4,000$ . Therefore, option C is correct, not B; the graph must be interpreted together with the stated rate.

Q8. A borrower claims that increasing the loan period from $2$ years to $4$ years doubles the principal needed to produce the same amount of interest at the same rate. Which statement best evaluates the claim?

A.It is correct because principal and time increase together.

B.It is incorrect because the required principal is cut in half. ✅

C.It is correct only when the rate exceeds

10\%

D.It is incorrect because principal remains unchanged.

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: From $P=\frac{I}{rt}$ , with interest and rate fixed, principal is inversely proportional to time. Doubling the time doubles the denominator, so the required principal becomes half as large rather than twice as large.

Q9. An investor wants to earn $\$1,080$ in simple interest. One option pays $6\%$ for $3$ years, while another pays $4.5\%$ for $4$ years. Which conclusion is correct about the required principals?

A.The first requires

\<span class="katex-error" title="ParseError: KaTeX parse error: Can&#x27;t use function &#x27;

' in math mode at position 7: 5,000 \̲)̲, while the sec…" style="color:#cc0000">5,000 \), while the second requires

\</span>6,000

B.Both require

\$6,000

. ✅

C.The first requires

\<span class="katex-error" title="ParseError: KaTeX parse error: Can&#x27;t use function &#x27;

' in math mode at position 7: 6,000 \̲)̲, while the sec…" style="color:#cc0000">6,000 \), while the second requires

\</span>5,000

D.Both require

\$4,000

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: For the first option, $P=1080/(0.06\cdot3)=\6,000 \). For the second, $P=1080/(0.045\cdot4)=\6,000$ . Although the rates and times differ, their products are both $0.18$ , producing equal required principals.

Q10. A student solves $1,050=P(0.07)(2)$ and obtains $P=\$7,350$ . Which error most likely caused the incorrect result?

A.The student multiplied by the rate instead of dividing.

B.The student treated

7\%

70\%

C.The student multiplied

1,050

0.14

instead of dividing by

0.14

. ✅

D.The student converted

2

years into months.

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Rearranging $1,050=P(0.14)$ requires division: $P=1,050/0.14=\$7,500$ . Multiplying $1,050$ by $0.14$ produces an amount far too small and reverses the algebraic relationship needed to isolate the principal.

Q11. A financial planner compares two loans that each charge $\$1,500$ in simple interest. Loan A uses $5\%$ for $5$ years, while Loan B uses $7.5\%$ for $4$ years. Which loan has the larger principal, and by how much?

A.Loan A by

\$1,000

✅

B.Loan B by

\$1,000

C.Loan A by

\$500

D.They have equal principals.

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: For Loan A, $P=1500/(0.05\cdot5)=\6,000 \). For Loan B, $P=1500/(0.075\cdot4)=\5,000$ . Thus Loan A is larger by $\$1,000$ , making option A correct; the comparison requires calculating both principals rather than comparing rates alone.

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