College Algebra Quiz: Simple Interest And Compound Interest
4 questions · exam conditions
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Simple Interest And Compound InterestQuestion 1 of 4

Two siblings inherit equal amounts and invest them differently. Alex invests his $20,000 at 5.5% compounded semi-annually. Jordan invests her $20,000 at a simple interest rate such that both investments have exactly the same value after 6 years. What simple interest rate does Jordan's investment earn?

Jordan's investment earns a simple interest rate of 6.18%
Jordan's investment earns a simple interest rate of 6.34%
Jordan's investment earns a simple interest rate of 6.49%
Jordan's investment earns a simple interest rate of 6.67%
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College Algebra Quiz

College Algebra Quiz: Simple Interest And Compound Interest

Practice Simple Interest And Compound Interest in College Algebra with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Simple Interest And Compound Interest, giving you a quick way to practice the rules, question types, and explanations that matter most for College Algebra.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

Two siblings inherit equal amounts and invest them differently. Alex invests his $20,000 at 5.5% compounded semi-annually. Jordan invests her $20,000 at a simple interest rate such that both investments have exactly the same value after 6 years. What simple interest rate does Jordan's investment earn?

  1. Jordan's investment earns a simple interest rate of 6.18%
  2. Jordan's investment earns a simple interest rate of 6.34%
  3. Jordan's investment earns a simple interest rate of 6.49% (correct answer)
  4. Jordan's investment earns a simple interest rate of 6.67%
Explanation: Alex's compound investment after 6 years: A=20,000(1+0.055/2)12=20,000(1.0275)12≈A = 20,000(1 + 0.055/2)^{12} = 20,000(1.0275)^{12} ≈ 27,790.12.ForJordan′ssimpleinteresttoequalthis:. For Jordan's simple interest to equal this: 27,790.12 = 20,000(1 + r × 6),so, so 1.389506 = 1 + 6r,giving, giving r = 0.389506/6 ≈ 0.0649$ or 6.49%. Choice A uses annual compounding for Alex, B uses incorrect time calculation, D assumes monthly compounding for Alex.

Question 2

An investment of $12,000 grows to $15,840 after 4 years under simple interest. If the same principal amount were invested at the same interest rate but compounded annually instead, what would be the difference in final amounts after the same 4-year period?

  1. The compound interest investment would yield $247.68 more than simple interest (correct answer)
  2. The compound interest investment would yield $312.45 more than simple interest
  3. The compound interest investment would yield $398.12 more than simple interest
  4. The compound interest investment would yield $425.76 more than simple interest
Explanation: First, find the simple interest rate: 15,840=12,000+12,000⋅r⋅415,840 = 12,000 + 12,000 \cdot r \cdot 4, so 3,840=48,000r3,840 = 48,000r, giving r=0.08r = 0.08 or 8%. For compound interest: A=12,000(1.08)4=12,000(1.36048896)=16,325.87A = 12,000(1.08)^4 = 12,000(1.36048896) = 16,325.87. The difference is $16,325.87 - 15,840 = 247.68247.68. Choice B uses incorrect compounding calculation, C assumes quarterly compounding, and D uses an inflated interest rate.

Question 3

A business loan of $75,000 accrues interest at 8.25% compounded quarterly. The borrower plans to pay off the loan in exactly 3 years but wants to know what single payment made after 18 months would reduce the final payment to exactly $35,000. What should this intermediate payment be?

  1. The intermediate payment should be approximately $54,250 (correct answer)
  2. The intermediate payment should be approximately $56,480
  3. The intermediate payment should be approximately $58,920
  4. The intermediate payment should be approximately $61,340
Explanation: After 18 months (6 quarters): A18=75,000(1.020625)6≈A_{18} = 75,000(1.020625)^6 ≈ 84,856.91.Weneedtheremainingbalanceafterpayment. We need the remaining balance after payment xtogrowtoexactly$35,000inthefinal18months:$(84,856.91−x)(1.020625)6=35,000 to grow to exactly $35,000 in the final 18 months: $(84,856.91 - x)(1.020625)^6 = 35,000. Solving: $84,856.91 - x = 35,000/(1.020625)^6 ≈ 35,000/1.1309 ≈ 30,95630,956. Therefore x≈84,856.91−30,956≈x ≈ 84,856.91 - 30,956 ≈ 53,901$, which is closest to choice A.

Question 4

An investment grows from $18,000 to $24,570 in 30 months under compound interest. If the interest is compounded monthly, what would the same principal amount grow to under simple interest at the same nominal annual rate after 42 months?

  1. Under simple interest, the investment would grow to approximately $25,890
  2. Under simple interest, the investment would grow to approximately $26,460 (correct answer)
  3. Under simple interest, the investment would grow to approximately $27,180
  4. Under simple interest, the investment would grow to approximately $27,720
Explanation: From compound interest: 24,570=18,000(1+r/12)3024,570 = 18,000(1 + r/12)^{30}, so (1+r/12)30=1.365(1 + r/12)^{30} = 1.365. Taking the 30th root: 1+r/12≈1.01081 + r/12 ≈ 1.0108, so r≈0.1296r ≈ 0.1296 or 12.96% annually. For simple interest over 42 months: A=18,000[1+0.1296×(42/12)]=18,000[1+0.1296×3.5]=18,000[1+0.4536]=18,000×1.4536≈A = 18,000[1 + 0.1296 × (42/12)] = 18,000[1 + 0.1296 × 3.5] = 18,000[1 + 0.4536] = 18,000 × 1.4536 ≈ 26,460$. Other choices use incorrect time conversions or rate calculations.