ASVAB interest and percent change problems
Simple interest is principal times rate times time (I = Prt). Percent change is the change divided by the original amount. Almost every money question on ASVAB Arithmetic Reasoning uses one of these two ideas, plus a few fraction-to-percent equivalents you can learn in an evening.
How do you calculate simple interest on the ASVAB?
Multiply principal by rate by time: I = P × r × t. Write the rate as a decimal and the time in years. Six months is 0.5 year.
Example: You put $3,000 in an account paying 4.5% simple interest for 2 years. How much interest do you earn?
- I = 3,000 × 0.045 × 2.
- Find 1% of 3,000: 30. Then 4.5% is 4.5 × 30 = 135.
- Two years: 135 × 2 = 270.
Answer: $270 in interest ($3,270 total)
Questions often ask for the total amount instead of the interest. Read the last sentence twice. The total is principal plus interest.
Example: A $5,000 loan costs $600 in simple interest over 3 years. What is the annual rate?
- Rearrange: r = I ÷ (P × t).
- P × t = 5,000 × 3 = 15,000.
- 600 ÷ 15,000 = 0.04.
Answer: 4% per year
What is the difference between simple and compound interest?
Simple interest is paid only on the original principal. Compound interest is paid on the principal plus the interest already earned, so it grows faster each period. On the ASVAB you can handle compound interest one year at a time.
Example: $2,000 earns 5% interest compounded once a year. How much is in the account after 2 years?
- Year 1 interest: 5% of 2,000 = 100. Balance: 2,100.
- Year 2 interest: 5% of 2,100 = 105. Balance: 2,205.
- Compare: simple interest would give 100 + 100 = 200, so $2,200.
Answer: $2,205
To take 5% of a number, take 10% (move the decimal one place) and halve it. 10% of 2,100 is 210, so 5% is 105.
How do you find percent increase and percent decrease?
Subtract to find the change, then divide by the original value. The original is the starting number, before the change happened.
Example: A part costs $40 and the price rises to $50. What is the percent increase? If it later drops from $50 back to $40, what is the percent decrease?
- Change: 50 − 40 = 10 in both directions.
- Increase: 10 ÷ 40 = 1/4 = 25%.
- Decrease: 10 ÷ 50 = 1/5 = 20%.
Answer: a 25% increase, then a 20% decrease
The same $10 change gives different percents because the starting amount differs. Test writers put both 20% and 25% in the choices, so check which number was first.
What happens with two percent changes in a row?
Apply them one after another to the new amount each time. You cannot add or cancel percents that apply to different bases.
Example: A $100 item is marked up 20%, then the new price is cut by 20%. What is the final price?
- After the markup: 100 × 1.20 = 120.
- After the cut: 120 × 0.80 = 96.
- Net change: 96 − 100 = −4, a 4% decrease.
Answer: $96
Multiplying by 1.20 for a 20% increase and by 0.80 for a 20% decrease is faster than finding the percent and then adding or subtracting.
How do you work backward to the original price?
Divide the final amount by the multiplier that produced it. After a 15% discount you pay 85% of the original, so the original is the sale price divided by 0.85.
Example: After a 15% discount, a jacket costs $68. What was the original price?
- Sale price = 0.85 × original.
- Original = 68 ÷ 0.85.
- Clear decimals: 6,800 ÷ 85 = 80.
- Check: 15% of 80 is 12, and 80 − 12 = 68.
Answer: $80
The trap answer adds 15% of the sale price back on: 68 + 10.20 = $78.20. That is wrong because the 15% was taken from the original, not from $68.
Example: An item costs $45 and sales tax is 8%. What is the total?
- 8% of 45: 1% is 0.45, so 8% is 3.60.
- Total: 45 + 3.60 = 48.60. Or 45 × 1.08 = 48.60.
Answer: $48.60
Which fraction, decimal and percent equivalents should you memorize?
Learn these so you can turn a percent into an easy fraction. 37.5% of 64 is hard; 3/8 of 64 is 24. The percentages lesson and fractions lesson have more drills.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33 1/3% |
| 2/3 | 0.666... | 66 2/3% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1666... | 16 2/3% |
| 5/6 | 0.8333... | 83 1/3% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/10 | 0.1 | 10% |
| 1/20 | 0.05 | 5% |
How do you calculate interest for months instead of years?
Convert the months into a fraction of a year before you use I = Prt. Divide the number of months by 12: 6 months is 0.5 year, 9 months is 0.75 year and 18 months is 1.5 years.
Example: You borrow $4,000 at 6% simple interest for 9 months. How much interest do you owe?
- Time in years: 9 ÷ 12 = 3/4 = 0.75.
- One full year of interest: 4,000 × 0.06 = 240.
- Three quarters of that: 240 × 3/4 = 180.
Answer: $180
If you plug in 9 as the time, you get $2,160, which is far larger than the loan's yearly interest. That kind of answer should make you stop and recheck the units. Interest for part of a year is always less than one year of interest.
How do you solve commission, markup and tip problems?
All three are "percent of" problems with a different name. A commission is a percent of sales, a markup is a percent added to cost, and a tip is a percent added to a bill.
Example: A salesperson earns $400 a week plus 5% commission on sales. One week the sales are $18,000. What are the total earnings?
- Commission: 5% of 18,000. 10% is 1,800, so 5% is 900.
- Add the base pay: 400 + 900 = 1,300.
Answer: $1,300
Example: A part costs a store $30 and is marked up 40%. What is the price?
- 40% of 30: 10% is 3, so 40% is 12.
- Price: 30 + 12 = 42. Or 30 × 1.40 = 42.
Answer: $42
Example: A meal costs $64. What is a 15% tip?
- 10% of 64 = 6.40.
- 5% is half of that: 3.20.
- 15% = 6.40 + 3.20 = 9.60.
Answer: $9.60
To find what percent one number is of another, divide the part by the whole. If you answered 18 of 24 questions correctly, 18 ÷ 24 = 3/4 = 75%. Simplify the fraction before you convert, and use the equivalents table above to turn it into a percent without long division.
How do you avoid common percent mistakes?
Most percent errors come from using the wrong base or answering a different question. Before you pick an answer:
- Identify the original amount. Percent change always divides by it.
- Decide whether the question wants the change (interest, discount) or the new total (balance, sale price).
- Convert percents to decimals before multiplying: 4% is 0.04, not 0.4.
- Estimate. A 6% interest charge on $800 should be a little under $50 per year.
Practice mixed problems in the math workout, and see the full formula sheet for the other money formulas.
Practice questions
Work each one on paper first, then open the explanation. These are original AptiStep items, not real ASVAB questions.
You borrow $800 at 6% simple interest for 3 years. How much interest do you pay?
- $48
- $144
- $944
- $128
Show answer and explanation
Answer: B. $144
I = P × r × t = 800 × 0.06 × 3. Six percent of 800 is 48 (1% is 8). Over 3 years: 48 × 3 = 144. The $48 choice is only one year, and $944 is the total repaid.
The price of a tool rises from $60 to $75. What is the percent increase?
- 20%
- 15%
- 25%
- 80%
Show answer and explanation
Answer: C. 25%
Change: 75 − 60 = 15. Divide by the original $60: 15 ÷ 60 = 1/4 = 25%. Dividing by the new price (15 ÷ 75 = 20%) is the most common error.
The price of a tool drops from $75 to $60. What is the percent decrease?
- 20%
- 25%
- 15%
- 80%
Show answer and explanation
Answer: A. 20%
Change: 75 − 60 = 15. The original price is now $75, so 15 ÷ 75 = 1/5 = 20%. Compare with the previous question: the same $15 change is 25% going up from 60 but 20% going down from 75.
$1,000 earns 10% interest compounded annually. What is the balance after 2 years?
- $1,200
- $1,100
- $1,221
- $1,210
Show answer and explanation
Answer: D. $1,210
Year 1: 10% of 1,000 = 100, balance 1,100. Year 2: 10% of 1,100 = 110, balance 1,210. The $1,200 choice uses simple interest, which ignores interest earned on the first year's interest.
After a 25% discount a pair of boots costs $54. What was the original price?
- $67.50
- $72
- $40.50
- $79
Show answer and explanation
Answer: B. $72
A 25% discount means you pay 75%, so original × 0.75 = 54. Original = 54 ÷ 0.75 = 54 × 4/3 = 72. Check: 25% of 72 is 18, and 72 − 18 = 54. The $67.50 choice adds 25% of $54, which uses the wrong base.
A $500 weekly pay is raised 10%, then later cut 10%. What is the new weekly pay?
- $495
- $500
- $490
- $505
Show answer and explanation
Answer: A. $495
After the raise: 500 × 1.10 = 550. After the cut: 550 × 0.90 = 495. The cut is 10% of 550, which is 55, larger than the 50 raise, so the pay ends $5 lower.
A town of 2,400 people grows by 15%. What is the new population?
- 2,415
- 2,640
- 2,760
- 360
Show answer and explanation
Answer: C. 2,760
10% of 2,400 is 240 and 5% is 120, so 15% is 360. New population: 2,400 + 360 = 2,760. The 360 choice is only the increase, and 2,640 is a 10% increase.
A $2,000 deposit earns $240 in simple interest over 2 years. What is the annual interest rate?
- 12%
- 4.8%
- 3%
- 6%
Show answer and explanation
Answer: D. 6%
r = I ÷ (P × t) = 240 ÷ (2,000 × 2) = 240 ÷ 4,000 = 0.06, or 6%. The 12% choice forgets to divide by the 2 years.
Frequently asked questions
Does the ASVAB use compound interest?
Interest questions are usually simple interest. If compounding is mentioned, work it one period at a time as shown above; you will not need an exponent formula with a calculator.
How do I find a percent of a number quickly?
Start from 10% (move the decimal one place left) and 1%, then build: 15% is 10% plus half of 10%, 6% is six times 1%. The mental math guide has more shortcuts.
What does "percent of" mean in an equation?
"Of" means multiply and "is" means equals. "What is 30% of 70" becomes x = 0.30 × 70 = 21.
Sources
Checked November 14, 2026. AptiStep is an independent study site; confirm anything that affects your enlistment with a recruiter.