Simple Interest Aptitude

Simple Interest is a fundamental concept in financial mathematics, commonly encountered in various competitive exams and real-world financial scenarios. It involves calculating the interest earned or paid on a principal amount over a period at a fixed interest rate. The formula for simple interest is I = PRT, where I is the interest, P is the principal amount, R is the rate of interest per year, and T is the time in years.

1. What is the simple interest on $2000 for 3 years at an annual interest rate of 5%?

Principal (P) = $2000, Rate (R) = 5%, Time (T) = 3 years.
Simple Interest (I) = PRT = 2000 * 5/100 * 3 = $300.

2. If the simple interest on a certain sum for 2 years at 4% per annum is $320, what is the principal amount?

Interest (I) = $320, Rate (R) = 4%, Time (T) = 2 years.
P = I / (RT) = 320 / (4/100 * 2) = $4000.

3. A sum of money becomes $1450 in 2 years and $1550 in 3 years on simple interest. What is the principal amount?

Interest for 1 year = 1550 - 1450 = $100.
For 2 years = $100 * 2 = $200.
Principal (P) = 1450 - 200 = $1250.

4. Find the rate of interest if $800 becomes $920 in 3 years at simple interest.

Principal (P) = $800, Amount = $920, Time (T) = 3 years.
Interest (I) = 920 - 800 = $120.
Rate (R) = I / (PT) = 120 / (800 * 3) = 5%.

5. If the simple interest on a sum for 4 years at 6% per annum is $240, what is the sum?

Interest (I) = $240, Rate (R) = 6%, Time (T) = 4 years.
Principal (P) = I / (RT) = 240 / (6/100 * 4) = $1000.

6. A sum of money doubles itself in 5 years at simple interest. What is the annual rate of interest?

Let the principal be P. It becomes 2P in 5 years.
Interest = 2P - P = P.
Rate (R) = (Interest / (Principal * Time)) * 100 = (P / (P * 5)) * 100 = 20%.

7. Find the simple interest on $5000 for 1.5 years at an annual interest rate of 8%.

Principal (P) = $5000, Rate (R) = 8%, Time (T) = 1.5 years.
Simple Interest (I) = PRT = 5000 * 8/100 * 1.5 = $600.

8. What principal will amount to $1120 in 4 years at a simple interest rate of 7% per annum?

Amount = $1120, Rate (R) = 7%, Time (T) = 4 years.
Interest (I) = Amount - Principal = 1120 - Principal.
Principal (P) = (I / (RT)) = (320 / (7/100 * 4)) = $800.

9. If the simple interest is $400 and the rate of interest is 5% per annum, find the principal if the time period is 4 years.

Interest (I) = $400, Rate (R) = 5%, Time (T) = 4 years.
Principal (P) = I / (RT) = 400 / (5/100 * 4) = $2000.

10. A sum fetched a total simple interest of $800 at the rate of 8% per annum in 5 years. What is the sum?

Interest (I) = $800, Rate (R) = 8%, Time (T) = 5 years.
Principal (P) = I / (RT) = 800 / (8/100 * 5) = $2000.

11. If $1500 is invested at a simple interest rate of 4% per annum, how much interest will be earned in 3 years?

Principal (P) = $1500, Rate (R) = 4%, Time (T) = 3 years.
Simple Interest (I) = PRT = 1500 * 4/100 * 3 = $180.

12. What is the total amount after 2 years if $2500 is invested at a simple interest rate of 6% per annum?

Principal (P) = $2500, Rate (R) = 6%, Time (T) = 2 years.
Interest (I) = PRT = 2500 * 6/100 * 2 = $300.
Total Amount = Principal + Interest = 2500 + 300 = $2900.

13. A person lent $2000 for 3 years and $3000 for 4 years on simple interest at the same rate and received a total interest of $1100. What was the annual rate of interest?

Total Interest (I) = $1100.
Interest for first sum = PRT = 2000 * R/100 * 3.
Interest for second sum = PRT = 3000 * R/100 * 4.
Total interest = 2000 * R/100 * 3 + 3000 * R/100 * 4 = 1100.
Solving, R = 5%.

14. A sum of money at simple interest amounts to $1200 in 2 years and to $1320 in 3 years. Find the sum.

Difference in amounts for 1 year = $1320 - $1200 = $120 (This is the interest for 1 year).
Principal (P) = Amount - Total Interest = 1200 - 2 * 120 = $1000.

15. If the simple interest on a certain sum for 6 months at 4% per annum is $120, what is the principal amount?

Interest (I) = $120, Rate (R) = 4%, Time (T) = 0.5 years (6 months).
Principal (P) = I / (RT) = 120 / (4/100 * 0.5) = $6000.

16. Find the simple interest on $8000 for 9 months at an annual interest rate of 6%.

Principal (P) = $8000, Rate (R) = 6%, Time (T) = 9/12 years (since 9 months).
Simple Interest (I) = PRT = 8000 * 6/100 * 9/12 = $360.

17. If the simple interest on a sum of money for 2 years at 5% per annum is $200, what is the sum?

Interest (I) = $200, Rate (R) = 5%, Time (T) = 2 years.
Principal (P) = I / (RT) = 200 / (5/100 * 2) = $2000.

18. A principal of $5000 is invested at a simple interest rate of 10% per annum. How much interest will it earn in 1.5 years?

Principal (P) = $5000, Rate (R) = 10%, Time (T) = 1.5 years.
Simple Interest (I) = PRT = 5000 * 10/100 * 1.5 = $750.

19. What is the total amount after 3 years if $4000 is invested at a simple interest rate of 7.5% per annum?

Principal (P) = $4000, Rate (R) = 7.5%, Time (T) = 3 years.
Interest (I) = PRT = 4000 * 7.5/100 * 3 = $900.
Total Amount = Principal + Interest = 4000 + 900 = $4900.

20. A sum of money amounts to $6200 in 2 years and to $7400 in 5 years at the same simple interest rate. What is the principal amount?

Interest for 3 years = $7400 - $6200 = $1200.
Annual Interest = $1200 / 3 = $400.
Total Interest for 2 years = 2 * $400 = $800.
Principal (P) = Amount - Total Interest for 2 years = 6200 - 800 = $5000.