If P stands for Principal, R the rate per cent per annum, T the number of years, I the simple interest and A the amount, then
1. Simple Interest = Principal Rate Time
100 or, I = P R T
100
Principal = 100 Simple Interest
Rate Time
or, P = 100 I
R T
3. Rate = 100 Simple Interest
Principal Time
or, R = 100 I
P T
4. Time = 100 Simple Interest
Rate Principal
or, T = 100 I
R P
5. Amount = Principal + Simple Interest
= Principal + Principal Rate Time
100
Some Useful Short-Cut Methods
1. If a certain sum in T years at R% per annum amounts to Rs. A, then the sum will be P = 100 A
100+RT
= Principal (1+(Rate Time)/100)
or, A = P (1 + (R T)/100)
2. The annual payment that will discharge a debt of Rs. A due in T years at R% per annum is Annual payment = Rs. (100A/(100T + RT(T – 1)/2))
3. If a certain sum is invested in n types of investments in such a manner that equal amount is obtained on each
investment where interest rates are R1, R2, R3, …, Rn respectively and time periods are T1, T2, T3, …, Tn
respectively, then the ratio in which the amounts are invested is
1/100+R1T1 : 1/100+R2T2
1/100+R3T3 : … 1/100+RnTn
4. If a certain sum of money becomes n times itself in T years at simple interest, then the rate of interest per annum is R = 100(n – 1)/T %
5. If a certain sum of money becomes n times itself at R% per annum simple interest in T years, then
6. If a certain sum of money becomes n times itself in T years at a simple interest, then the time T in which it will become m times itself is given by
T = (m – 1/n – 1) T years.
7. Effect of change of P, R and T on simple interest is given by the following formula:
= Product of fixed parameter/100 [difference of product of variable parameters]
for example, if rate ® changes from R1 to R2
and P, T are fixed then Change in SI = PT/100 (R1 – R2)
Similarly, if principal (P) changes from P1 to P2 and R, T are fixed, then change in SI = RT/100 (P1 – P2)
Also, if rate ® changes from R1 to R2 and time (T) changes from T1 to T2 but principal (P) is fixed, then
change in SI = P/100 (R1T1 – R2T2).
8. If a debt of Rs. Z is paid in ‗n‘ number of instalments and if the value of each instalment is Rs. a, then the borrowed (debt) amount is given by
Z = na + (Ra/100 b) n(n – 1)/2 Where, R = rate of interest per annum
b = no. of instalments/year
b = 1, when each instalment is paid yearly b = 2, when each instalment is paid half-yearly b = 4, when each instalment is paid quarterly b = 12, when each instalment is paid monthly.
9. If a certain sum of money P lent out at SI amounts to A1 in T1 years and to A2 in T2 years, then
P = A1T2 – A2T1
T2 – T1
and, R = A1 – A2/A1T2 - A2T1 100%
10. If a certain sum of money P lent out for a certain time T amounts to A1 at R1% per annum and to A2 at R2% per
annum, then
P = A2R1 – A1R2/R1 – R2
and, T = A1 – A2 100 years.
A2R1-A1R2
11. If an amount P1 lent at simple interest rate of R1% per annum and another amount P2 at simple interest rate of
R2% per annum, then the rate of interest for the whole sum is R = (P1R1+P2R2/P1+P2).
12. If a certain sum of money is lent out in n parts in such a manner that equal sum of money is obtained as simple
interest on each part where interest rates are R1, R2, …, Rn respectively and time periods are T1, T2, …, Tn
respectively, then the ratio in which the sum will be divided in n parts is given by 1/R1T1 : 1/R2T2 : …1/RnTn
13. When there is a change in principal (P), Rate (R) and Time (T), then the value of simple interest I also changes and is given by
I1/I2 = P1 R1 T1/P2 R2 T2
A1 – P1/A2 – P2 = P1 R1 T1/P2 R2 T2
14. Out of a certain sum P, 1/a part is invested at R1%, 1/b part at R2% and the remainder (1-1/a-1/b) say 1/c part at
R3%. If the annual income from all these investments is Rs. A, then the original sum is given by
P = ((A 100)/R1/A+R2/B+R3/C)
EXERCISE
1. Interest obtained on a sum of Rs.5000 for 3 years is Rs.1500. Find the rate percent.
1. 8% 2. 9% 3. 10% 4. 11%
2. Rs.2100 is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.
1. 2300/- 2. 2315.25/- 3. 2310/- 4. 2320/-
3. Find the difference between the simple and he compound interest at 5% per annum for 2 years on a principal of Rs.2000.
1. 5 2. 105 3. 4.5 4. None
4. After how many years will a sum of Rs.12,500 become Rs.17, 500 at the rate of 10% per annum?
1. 2 years 2. 3 years 3. 4 years 4. 5 years
5. What is the difference between the simple interest on a principal of Rs.500 being calculated at 5% per annum for 3 years and 4% per annum for 4 years?
1. 5/- 2. 10/- 3. 20/- 4. 40/-
6. What is the difference between compound interest and simple interest for the sum of Rs.2000 over a 2 year period if the compound interest is calculated at 20% and simple interest is calculated at 23%
1. 40/- 2. 46/- 3. 44/- 4. None
7. Find the compound interest on Rs.1000 at the rate of 20% per annum for 18 months when interest is compounded half-yearly?
1. 331/- 2. 1331/- 3. 320/- 4. None
8. Find the principal if compound interest is charged on the principal at the rate of 16 2/3% per annum for two years and the sum becomes Rs.196.
1. 140/- 2. 154/- 3. 150/- 4. None
9. The SBI lent Rs.1331 to the Tata group at a compound interest and got Rs.1728 after three years. What is the rate of interest charged if the interest is compounded annually?
1. 11% 2. 9.09% 3. 12% 4. 8.33%
10. Varun purchased a Maruti van for Rs.1, 96,000 and the rate of depreciation is 14 2/7% per annum. Find the value of he van after two years.
1. 1, 40, 000/- 2. 1, 44, 000/- 3. 1, 50, 000/- 4. None
11. Varun deposited Rs.8000 in ICICI Bank, which pays him 12% interest per annum compounded quarterly. What is the amount that he receives after 15 months?
12. What is he rate of simple interest for the first 4 years if the sum of Rs.360 becomes Rs.540 in 9 years and the rate of interest for the last 5 years is 6%?
1. 4% 2. 5% 3. 3% 4. 6%
13. Havishma makes a fixed deposit of Rs.20,000 with the Bank of India for a period of 3 years. If the rate of interest be 13% SI per annum charged half-yearly, what amount will he get after 42 months?
1. 27, 800/- 2. 28, 100/- 3. 29, 100/- 4. None
14. Varun makes a deposit of Rs.50,000 in the Punjab National Bank for a period of 2 ½ years. If the rate of interest is 12% per annum compounded half-yearly, find the maturity value of the money deposited by him.
1. 66, 911.27 2. 66, 123.34 3. 67, 925.95 4. 65, 550.8
15. Varun borrows Rs.1500 from two money lenders. He pays interest at the rate of 12% per annum for one loan and at he rate of 14% per annum for the other. The total interest he pays for the entire year is Rs.186.How much does he borrow at he rate of 12%?
1. 1200/- 2. 1300/- 3. 1400/- 4. 300/-
16. Two equal sums were borrowed at 8% simple interest per annum for 2 years and 3 years respectively. The difference in the interest was Rs.56. the sum borrowed were
1. 690/- 2. 700/- 3. 740/- 4. 780/-
17. In what time will Rs.500 give Rs.50 as interest at the rate of 5% per annum simple interest?
1. 2 years 2. 5 years 3. 3 years 4. 4 years
18. Shashikant derives an annual income of Rs.688.25 from Rs.10,000 invested partly at 8% p.a. and partly at 5% p.a. simple interest. How much of his money is invested at 5%?
1. 5, 000/- 2. 4225/- 3. 4, 8000/- 4. 3, 725/-
19. If the difference between the simple interest and compound interest on some principal amount at 20% per annum for 3 years is Rs.48, then the principal amount must be
1. 550/- 2. 500/- 3. 375/- 4. 400/-
20. Raju lent Rs.400 to Ajay for 2 years, and Rs.100 to Manoj for 4 years and received together from both Rs.60 as interest. Find the rate of interest, simple interest being calculated.
1. 5% 2. 6% 3. 8% 4. 9%
21. In what time will Rs.8000 amount to 40,000 at 4% per annum? (simple interest being reckoned)
1. 100 years 2. 50 years 3. 110 years 4. 160 years
22. What annual payment will discharge a debt of Rs.808 due in 2 years at 2% per annum?
1. 200/- 2. 300/- 3. 400/- 4. 350/-
23. A sum of money doubles itself in 5 years. In how many years will it become four fold (If interest is compounded)?
1.15 2. 10 3. 20 4. 12
24. Divide Rs.6000 into two parts so that simple interest on the first part for 2 years at 6% p.a. may be equal to the simple interest on the second part for 3 years at 8% p.a.
1. 4000/-, 2000/- 2. 5000/-, 1000/- 3. 3000/-, 3000/- 4. None
25. A sum of money becomes 7/4 of itself in 6 years at a certain rate of simple interest. Find the rate of interest
1. 12% 2. 12(1/2)% 3. 8% 4. 14%
26. Samjay borrowed Rs.900 at 4% p.a. and Rs.1100 at 5% p.a. for the same duration. He had to pay Rs.364 in all as interest. What is the time period in years?
1. 5 years 2. 3years 3. 2 years 4. 4 years
27. If the difference between compound and simple interest on a certain sum of money for 3 years at 2% p.a. is Rs.604, what is the sum?
1. 500, 000 2. 450, 000 3. 510, 000 4. None
28. If a certain sum of money becomes double at simple interest in 12 years, what would be the rate of interest per annum?
1. 8(1/3) 2. 10 3. 12 4. 14
29. Three persons Amar, Akbar and Anthony invested different amounts in a fixed deposit scheme for one year at the rate of 12% per annum and earned a total interest of Rs.3, 240 at the end of the year. If the amount invested by Akbar is Rs.5000 more than the amount invested by Amar is Rs.5000 more than the amount invested by Amar and the amount invested by Anthony is Rs.2000 more than the amount invested by Akbar, what is the amount invested by Akbar?
1. 12, 000/- 2. 10, 000/- 3. 7, 000/- 4. 5000/-
30. A sum of Rs.600 amounts to Rs.720 in 4 years at Simple Interest. What will it amount to if the rate of interest is increased by 2%