Asked by Utibe
Give me questions on simple interest without putting amount
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Here are 20 simple-interest practice questions that do not give any monetary amounts (they use words or variables instead). No numeric principal is specified — solve symbolically or using relationships.
Basic / straightforward
1. A sum at simple interest earns interest I in 3 years at r% per annum. Express I in terms of the principal P, r and time.
2. If a sum is invested at simple interest at r% per annum for t years, what is the total amount A in terms of P, r and t?
3. The simple interest on a sum for 2 years equals the simple interest on the same sum for 5 years. What must r be? (Interpret the statement and explain why it is or is not possible.)
4. The simple interest on a sum for 1 year equals half the simple interest for 2 years. Is this always true? Explain.
Solve-for-rate / time / principal relations
5. Simple interest on a sum for 4 years at rate r% equals simple interest on the same sum for 6 years at rate s%. Find the ratio r : s.
6. The simple interest on a sum for 3 years at r% equals the simple interest on another sum for 3 years at s%. If the second sum is twice the first, find the relation between r and s.
7. A sum invested at r% simple interest for t years yields interest equal to half the principal. Express t in terms of r.
8. Simple interest for 5 years at r% equals one-third of the principal. Find r in terms of P and time (or express r numerically if t is given symbolically).
Word-problem style (no amounts)
9. Two sums are invested at the same simple interest rate. One is invested for 2 years and the other for 5 years. If the interest earned by the first is I1 and by the second is I2, express I1 : I2 and explain.
10. A borrower repays with simple interest such that the interest equals the original sum after 10 years. What annual rate r achieves this?
11. A sum triples (i.e., amount becomes three times the principal) under simple interest. If this happens in t years, find r in terms of t.
12. The interest earned on a sum for 2 years at r% is equal to the interest earned on twice that sum for 3 years at s%. Find the relationship between r and s.
Algebra / system problems
13. Two different rates r and s (r > s) applied as simple interest on the same principal for 2 years and 5 years respectively produce equal interest amounts. Solve for r in terms of s.
14. Three sums, in the ratio 1 : 2 : 3, are invested at the same simple interest rate for the same period. If the total interest earned is I_total, express the interest earned on the largest sum in terms of I_total.
15. A sum at r% simple interest for 2 years yields interest I. The same sum at (r + 2)% for 3 years yields interest 2I. Find r.
Application / comparison
16. A sum placed at simple interest for 4 years yields the same interest as it would at compound interest for 3 years at the same nominal rate r. Describe how you would set up an equation to compare the two (no numeric amounts required).
17. Two investments at simple interest yield interests in the ratio 4 : 7 for the same period. If their principals are in the ratio 3 : k, find k.
18. The simple interest earned on a sum for the first 2 years is A and for the next 3 years is B. How are A and B related? (Express A : B.)
Challenge / reasoning
19. Explain whether a sum under simple interest can ever double in less than 5 years if the rate is less than 20% per annum.
20. Without giving a principal, show how to determine the time needed for a principal to gain an amount of interest equal to x times the principal under simple interest at rate r% per annum.
If you want, I can:
- Provide numeric versions of any selected question (with amounts) for calculation practice.
- Solve any of the above symbolically or numerically.
- Convert these into multiple-choice or worksheet format. Which would you like next?
Basic / straightforward
1. A sum at simple interest earns interest I in 3 years at r% per annum. Express I in terms of the principal P, r and time.
2. If a sum is invested at simple interest at r% per annum for t years, what is the total amount A in terms of P, r and t?
3. The simple interest on a sum for 2 years equals the simple interest on the same sum for 5 years. What must r be? (Interpret the statement and explain why it is or is not possible.)
4. The simple interest on a sum for 1 year equals half the simple interest for 2 years. Is this always true? Explain.
Solve-for-rate / time / principal relations
5. Simple interest on a sum for 4 years at rate r% equals simple interest on the same sum for 6 years at rate s%. Find the ratio r : s.
6. The simple interest on a sum for 3 years at r% equals the simple interest on another sum for 3 years at s%. If the second sum is twice the first, find the relation between r and s.
7. A sum invested at r% simple interest for t years yields interest equal to half the principal. Express t in terms of r.
8. Simple interest for 5 years at r% equals one-third of the principal. Find r in terms of P and time (or express r numerically if t is given symbolically).
Word-problem style (no amounts)
9. Two sums are invested at the same simple interest rate. One is invested for 2 years and the other for 5 years. If the interest earned by the first is I1 and by the second is I2, express I1 : I2 and explain.
10. A borrower repays with simple interest such that the interest equals the original sum after 10 years. What annual rate r achieves this?
11. A sum triples (i.e., amount becomes three times the principal) under simple interest. If this happens in t years, find r in terms of t.
12. The interest earned on a sum for 2 years at r% is equal to the interest earned on twice that sum for 3 years at s%. Find the relationship between r and s.
Algebra / system problems
13. Two different rates r and s (r > s) applied as simple interest on the same principal for 2 years and 5 years respectively produce equal interest amounts. Solve for r in terms of s.
14. Three sums, in the ratio 1 : 2 : 3, are invested at the same simple interest rate for the same period. If the total interest earned is I_total, express the interest earned on the largest sum in terms of I_total.
15. A sum at r% simple interest for 2 years yields interest I. The same sum at (r + 2)% for 3 years yields interest 2I. Find r.
Application / comparison
16. A sum placed at simple interest for 4 years yields the same interest as it would at compound interest for 3 years at the same nominal rate r. Describe how you would set up an equation to compare the two (no numeric amounts required).
17. Two investments at simple interest yield interests in the ratio 4 : 7 for the same period. If their principals are in the ratio 3 : k, find k.
18. The simple interest earned on a sum for the first 2 years is A and for the next 3 years is B. How are A and B related? (Express A : B.)
Challenge / reasoning
19. Explain whether a sum under simple interest can ever double in less than 5 years if the rate is less than 20% per annum.
20. Without giving a principal, show how to determine the time needed for a principal to gain an amount of interest equal to x times the principal under simple interest at rate r% per annum.
If you want, I can:
- Provide numeric versions of any selected question (with amounts) for calculation practice.
- Solve any of the above symbolically or numerically.
- Convert these into multiple-choice or worksheet format. Which would you like next?
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