1. At the same annual interest rate, the compound interest and simple interest on a principal amount will be equal.
(a) 1 years (b) 2 years (c) 3 years (d) 4 years
2. At the same annual percentage interest rate, the simple interest and compound interest on a principal amount become equal in _____ years (interest period: 1 year).
3. For a fixed amount of money, at a fixed annual rate of interest, the compound interest and simple interest will be equal in -- years.
4. In how many years will the amounts of simple interest and compound interest be equal for the same principal at the same annual interest rate?
(a) 3 years (b) 2 years (c) 1 years (d) \(\frac{1}{2}\)
5. For a fixed amount of money at a fixed annual interest rate, the amount of compound interest and simple interest after 1 year will be equal.
6. At an equal annual interest rate, determine the number of years required for the simple interest and compound interest on a given principal to become equal.
7. If the time period and the annual simple interest rate are equal, then at what annual interest rate will the interest amount be \(\cfrac{1}{25}\) of the principal?
(a) 25% (b) 10% (c) 2% (d) 2.5%
8. ₹1200 is lent at an annual interest rate of 6\(\frac{1}{4}\)% and ₹1000 is lent at an annual interest rate of 4\(\frac{1}{3}\)% on the same day. After how much time will the amounts (principal + interest) of both loans become equal?
(a) 20 years (b) 24 years (c) 15 years (d) 30 years
9. If the simple interest on ₹850 for 3 years and on ₹1250 for 4 years at the same rate amounts to ₹302 in total, then what will be the annual rate of interest?
(a) 3% (b) 5% (c) 7% (d) None of the above
10. At an annual percentage rate of interest, the simple interest and compound interest on a principal amount are equal after —— years.
11. Which one will be less: the simple interest for 2 years or the compound interest with annual compounding for 2 years, on a fixed principal, if the rate of interest is the same?
12. Mr. Amal bequeaths ₹56,000 in his will for his two sons aged 13 and 15 in such a way that, when they each turn 18, the simple interest earned at an annual rate of 10% will be equal to the principal for each. What will be the allocated amount for each son in the will?
13. If the simple interest on a certain amount at an annual interest rate of 8% for 2 years is ₹850, then what will be the compound interest for the same period?
(a) ₹ 1684 (b) ₹984 (c) ₹ 884 (d) none of the above
14. At an annual interest rate of 20%, for how much principal will the difference between compound interest and simple interest for 3 years be ₹1024?
(a) ₹ 2800 (b) ₹ 1100 (c) ₹ 8000 (d) ₹ 3000
15. If the annual interest rate is the same, the compound interest on a principal amount for one year will be higher than the simple interest.
16. Anil Babu wants to allocate ₹56,000 between his two sons, aged 13 and 15, such that when they turn 18, the simple interest earned at an annual rate of 10% is equal to their respective principal amounts. Determine the amount allocated to each son in the will.
17. My aunt wants to will 56,000 INR between her two sons, aged 13 and 15, in such a way that when they turn 18, the total amount received (principal + interest) for each son will be equal, given a 10% annual simple interest rate. Determine the amount allocated for each son in the will.
18. If the compounding period is 1 year, the simple interest and compound interest for 1 year on a certain amount of money will be equal.
19. If the annual compound interest rate is \(r\%\), and the interest earned is _____, then the compound amount of \(p\) rupees in \(n\) years will be \(p\left(1+\cfrac{r}{400}\right)^{4n}\) rupees.
20. At an annual interest rate of 5%, what will be the difference between compound interest and simple interest for ₹20,000 over 2 years?
21. My aunt wants to will ₹56,000 between her two sons, aged 13 and 15, in such a way that by the time each turns 18, the total amount (principal + interest) received by both sons is equal. The interest is calculated at an annual simple interest rate of 10%. Determine how much should be allotted to each son in the will.
22. At an annual interest rate of 4%, for how much money will the difference between the simple interest and the compound interest for 2 years be 80 rupees? Let’s calculate and write it down.
23. If the annual interest rate and time period are equal, in how many years will the interest on 144 rupees become 25 rupees?
(a) 4 years (b) \(4\cfrac{1}{6}\) years (c) 6 years (d) \(6\cfrac{1}{4}\) years
24. Under the same simple interest rate, a principal amount grows to 7000 rupees in 5 years and 8200 rupees in 8 years. What is the rate of interest?
(a) 4% (b) 6% (c) 8% (d) 10%
25. If a sum of money becomes 4 times its original amount in *n* years at a fixed annual compound interest rate, then in how many years will it become 4 times?
26. If a sum of money doubles in \(n\) years at a fixed annual compound interest rate, then in how many years will it become 4 times?
27. At an annual interest rate of 4%, what principal amount will yield at least ₹80 difference between simple interest and compound interest over 2 years?
28. If the simple interest for \(n\) years at an annual rate of \(r\%\) is \(\frac{pnr}{25}\) rupees, then the principal amount will be _____ rupees.
29. At an annual rate of 10%, the difference between the simple interest and compound interest on ₹100 for 1 year is ₹1.
30. If interest is compounded every 6 months, then at an annual compound interest rate of 10%, what will be the compound amount and compound interest on ₹8000 for 1½ years?
