Questions: Simple Interest

Question 1

You deposit $1,000 at 5% simple annual interest for 3 years. How much interest have you earned?

• A. $157.63 — interest compounds each year on the growing balance
• B. $150 — interest is calculated only on the original $1,000 each year
• C. $50 — you earn 5% total over the 3 years, not per year
• D. $15 — 5 and 3 multiply to 15, applied directly as dollars

Answer: (B)

Using I = Prt: I = 1000 × 0.05 × 3 = $150. Simple interest is calculated on the original principal every year — $50 per year for 3 years = $150 total. Option A shows compound interest, where interest earns additional interest each year. Option C misapplies the rate as a total rather than an annual rate. Option D confuses the rate value with a dollar amount and forgets the decimal conversion.

Question 2

A student calculates simple interest on a $200 loan at 3% for 2 years by computing 200 × 3 × 2 = 1,200. What error did the student make?

• A. Used the wrong formula — should have added the values instead of multiplied
• B. Did not convert the interest rate from percent to decimal (should use 0.03, not 3)
• C. Used the wrong time period — 2 years should be converted to 24 months first
• D. Forgot to add the principal to the interest at the end to get the total amount

Answer: (B)

The student used r = 3 instead of r = 0.03, making the answer 100 times too large. The formula requires the rate as a decimal: 3% = 0.03. Correct calculation: I = 200 × 0.03 × 2 = $12. The percent-to-decimal conversion is the most common computational error in simple interest problems — using the raw percent number instead of its decimal equivalent inflates the result by a factor of 100.

Question 3

If you borrow money at simple interest, doubling the loan period doubles the total interest owed.

• T. True
• F. False

Answer: True

Simple interest grows linearly with time because interest is always calculated on the same original principal. If I = Prt, and you double t, you get I = Pr(2t) = 2(Prt) — exactly double the interest. This linear relationship is the defining characteristic of simple interest. It contrasts directly with compound interest, where doubling the time more than doubles the interest because of exponential growth.

Question 4

With simple interest, more interest is earned in year 3 than in year 1, because the account has grown larger over time.

• T. True
• F. False

Answer: False

This describes compound interest, not simple interest. In simple interest, the same dollar amount of interest is earned every year because interest is always calculated on the original principal — never on previously accumulated interest. In year 1, year 2, and year 3, you earn exactly P × r. The account grows linearly — the graph of total value over time is a straight line, not a curve upward.

Question 5

What does 'simple' mean in 'simple interest,' and how does this make its growth pattern different from compound interest?

Model answer: 'Simple' means interest is calculated only on the original principal each period — it never earns interest on itself. This makes growth linear: the same fixed dollar amount accumulates each year. Compound interest, by contrast, applies the rate to the growing balance (principal plus previously earned interest), so each year's interest is larger than the last, producing exponential growth.

The practical effect is small over short periods but dramatic over long ones. A $1,000 deposit at 5% simple interest earns $50 every year forever. At 5% compound interest, year 1 earns $50, year 10 earns about $77, and year 30 earns about $208. The word 'simple' is the signal that no compounding occurs — the interest calculation resets to the same base every period.