College Algebra Quiz: Simple Interest And Compound Interest

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.

Question 1

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} ≈$27,790.12$. For Jordan's simple interest to equal this:$27,790.12 = 20,000(1 + r × 6)$, so$1.389506 = 1 + 6r$, 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

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: $15,840 = 12,000 + 12,000 \cdot r \cdot 4$, so $3,840 = 48,000r$, giving $r = 0.08$ or 8%. For compound interest: $A = 12,000(1.08)^4 = 12,000(1.36048896) = 16,325.87$. The difference is $16,325.87 - 15,840 =$247.68$. Choice B uses incorrect compounding calculation, C assumes quarterly compounding, and D uses an inflated interest rate.

Question 3

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): $A_{18} = 75,000(1.020625)^6 ≈$84,856.91$. We need the remaining balance after payment$x$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 ≈$30,956$. Therefore$x ≈ 84,856.91 - 30,956 ≈ $53,901$, which is closest to choice A.

Question 4

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: $24,570 = 18,000(1 + r/12)^{30}$, so $(1 + r/12)^{30} = 1.365$. Taking the 30th root: $1 + r/12 ≈ 1.0108$, so $r ≈ 0.1296$ 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 ≈$26,460$. Other choices use incorrect time conversions or rate calculations.