INTEREST
Relation Among Principal, Time, Rate Percent of Interest Per Annum and Total Interest
Formula
Case 1 : Let principal = P, time = n years and rate = 4% per annum and let A be the total amount at
Case 2 : When compound interst is reckoned half=yearly. If the annual rate is r% per annum and is to be calculated for n years.
Then in this case, rate = (r/2)% half-yearly and time = (2n) half-years.\ From the above we get
Case 3 : When compound interest is reckoned quarterly. In this case, rate = (r/4)% quarterly and time = (4n) quarter years.
\ As before,
Note: The difference between the compound interest and the simple interest over two years is given by
Depreciation of value
The value of a machine or any other article subject to wear and tear, decreases with time. This decrease is called its
depreciation. Thus if V0 is the value at a certain time and r% per annum is the rate of depreciation per year, then the value
Ex.1 The rate of interest for first 3 years is 6% per annum, for the next 4 years, 7 per cent per annum and for the period beyond 7 years, 7.5
percentages per annum. If a man lent out Rs. 1200 for 11 years, find the total interest earned by him ?
(A) Rs. 1002 (B) Rs. 912
(C) Rs. 864 (D) Rs. 948
ASSIGNMENT
1. Rs. 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.
(A) Rs. 1380 (B) Rs. 1290
(C) Rs. 1470 (D) Rs. 1200
(E) Rs. 1240
2. Interest obtained on a sum of Rs. 5000 for 3 years is Rs. 1500. Find the rate percent.
(A) 8% (B) 9%
(C) 10% (D) 11%
(E) 12%
3. Rs. 2100 is lent at compound interst of 5% per annum for 2 years. Find the amount after two years.
(A) Rs. 2300 (B) Rs. 2315.25
(C) Rs. 2310 (D) Rs. 2320
(E) None of these
4. If a certain sum of money becomes double at simple interest in 12 years, what would be the rate of interst per annum ?
(A) 8(3/1) (B) 10
(C) 12 (D) 14
5. Three person 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. 3240 at the end of the year. If the amount invested by Akbar is Rs. 5000 more than the amount invested
by Amar and teh amount invested by Anthony is Rs. 2000 more than the amount investd by Akbar, what is the amount invested by Akbar ?
(A) Rs. 12,000 (B) Rs. 10,000
(C) Rs. 7000 (D) Rs. 5000
6. 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% ?
(A) Rs. 648 (B) Rs. 768
(C) Rs. 648 (D) Rs. 792
7. What is the amount of equal instalment, if a sum of Rs. 1428 due 2 years hence has to be completely repaid in 2 equal annual instalments starting next year.
(A) 700 (B) 800
(C) 650 (D) Cannot be determined
8. A sum of money invested at simple interest triples itself in 8 years at simple interst. Find in how many years will it become 8 times itself at the same rate ?
(A) 24 years (B) 28 years
(C) 30 years (D) 21 years
(D) 25 years
9. A sum of money invested at simple interst triples itself in 8 years. How many times will it become in 20 years time ?
(A) 8 times (B) 7 times
(C) 6 times (D) 9 times
(E) None of these
Directions for Questions 10 – 11 : Read the following and answer the questions that follow.
10. A certain sum of money was lent under teh following repayment scheme based on simple interest:
8% per annum for the initial 2 years
9.5% per annum for the next 4 years
11% per annum for the next 2 years
12% per annum after the first 8 years
Find the amount which a sum of Rs. 9000 taken for 12 years becomes at the end of 12 years.
(A) 20,200 (B) 19,800
(C) 20,000 (D) 20,160
(D) None of these
11. If a person repaid Rs. 22,500 after 10 years of borrowing a loan, at 10% per annum simple interst find out what amount did he take as a loan ?
(A) 11,225 (B) 11,250
(C) 10,000 (D) 7500
(E) None of these
12. A person lent out some money for 1 years at 6% per annum simple interest and after 18 months, he again lent out the same money at a simple
interest of 24% per annum. In both the cases, he got Rs. 4704. Which of these could be the amount that was lent out in each case if interest is paid half-yearly ?
(A) Rs. 4000 (B) Rs. 4400
(C) Rs. 4200 (C) Rs. 3600
(E) Rs. 3800
13. A person bought a motorbike under the following scheme: Down payment of Rs. 15,000 and the rest amount at 8% per annum for
2 years. In this way, he paid Rs. 28,920 in total. Find the actual price of the motorbike. (Assume simple interst).
(A) Rs. 26,000 (B) Rs. 27,000
(C) Rs. 27,200 (D) Rs. 26,500
(E) Rs. 28,000
14. Hans Kumar borrows Rs. 7000 at simple interest from the village moneylender. At te end of 3 years, he again borrows Rs. 3000 and closes his
account after paying Rs. 4615 as interest after 8 years from the time he made the first borrowing. Find the rate of interst.
(A) 3.5% (B) 4.5%
(C) 5.5% (D) 6.5%
(E) 5%
15. Some amount was lent at 6% per annum simple interest. After one year, Rs 6800 is repaid and the rest of the amount is repaid at 5% per
annum. If the second years' interst is 11/20 of the first years' interest, find what amoung of money was lent out.
(A) Rs. 17,000 (B) Rs. 16,800
(C) Rs. 16,500 (D) Rs. 17,500
(E) None of these
16. An amount of Rs. 12820 due 3 years hence, is fully repaid in three annual instalments starting after 1 year. The first instalment is
1/2 the second instalment and the second instalment is 2/3 of the third instalment. If the rate of interst is 10% per annum, find the first instalmen.
(A) Rs. 2400 (B) Rs. 2800
(C) Rs. 2000 (D) Rs. 2500
ANSWER KEY
1) A 2) C 3) B 4) A 5) B 6) B 7) D 8) B
9) C 10) D 11) B 12) C 13) B 14) D 15) A 16) C