Compound Interest Set 1

1. On a certain sum of money, after 2 years the simple interest and compound interest obtained are Rs 800 and Rs 960 respectively. What is the sum of money invested?
   A) Rs 1420
   B) Rs 1325
   C) Rs 1000
   D) Rs 1405
   E) Rs 1375
   
   C) Rs 1000
   Explanation:
   Diff = 960-800 = 160
   r = 2*Diff*100/SI
   So r = 2*160*100/800 = 40%
   Now 160 = Pr2/1002
   
   
   
2. Rs 6000 becomes Rs 7200 in 3 years at a certain rate of compound interest. What will be the amount received after 9 years?
   A) Rs 11,498
   B) Rs 10,352
   C) Rs 9,368
   D) Rs 10,368
   E) None of these
   
   D) Rs 10,368
   Explanation:
   6000[1 + r/100]3 = 7200
   So [1 + r/100]3 = 6/5
   So 6000[1 + r/100]9 = 6000*(6/5)*(6/5)*(6/5)
   
   
3. A man borrows Rs 4000 at 8% compound interest for 3 years. At the end of each year he paid Rs 500. How much amount should he pay at the end of 3rd year to clear the debt?
   A) Rs 4254.5
   B) Rs 3465.2
   C) Rs 3485.2
   D) Rs 4345.4
   E) Rs 3915.6
   
   E) Rs 3915.6
   Explanation:
   Amount after 1 yr = 4000[1 + 8/100] = 4320
   Paid 500, so P = 4320 – 500 = 3820
   Amount after 2nd yr = 3820[1 + 8/100] = 4125.6
   So P= 4125.6-500 = 3625.6
   Amount after 3rd yr = 3625.6[1 + 8/100] = 3915.6
   
   
   
4. A sum of money is lent for 2 years at 20% p.a. compound interest. It yields Rs 482 more when compounded semi-annually than compounded annually. What is the sum lent?
   A) Rs 25,600
   B) Rs 20,000
   C) Rs 26,040
   D) Rs 40,500
   E) None of these
   
   B) Rs 20,000
   Explanation:
   P[1 + (r/2)/100]4 – P[1 + r/100]2 = 482
   P[1 + 10/100]4 – P[1 + 20/100]2 = 482
   Solve, P = 20,000
   
   
5. The compound interest obtained after 1st and 2nd year is Rs 160 and Rs 172.8 respectively on a certain sum of money invested for 2 years. What is the rate of interest?
   A) 10%
   B) 8%
   C) 8.5%
   D) 9%
   E) 9.2%
   
   B) 8%
   Explanation:
   Difference in interest for both yrs = 172.8 – 160 = 12.8
   So (r/100)*160 = 12.8
   
   
   
6. A sum of money becomes Rs 35,280 after 2 years and Rs 37,044 after 3 years when lent on compound interest. Find the principal amount.
   A) Rs 32,000
   B) Rs 28,000
   C) Rs 31,500
   D) Rs 32,500
   E) None of these
   
   A) Rs 32,000
   Explanation:
   P[1 + r/100]3 = 37,044, and P[1 + r/100]2 = 35,280
   Divide both equations, [1 + r/100] = 37044/35280 = 21/20
   So P[21/20]2 = 35280
   
   
7. The difference between compound interest earned after 3 years at 5% p.a. and simple interest earned after 4 years at 4% p.a. is Rs 76. Find the principal amount.
   A) Rs 32,000
   B) Rs 28,000
   C) Rs 31,500
   D) Rs 32,500
   E) None of these
   
   A) Rs 32,000
   Explanation:
   [P[1 + 5/100]3 – P] – P*4*4/100 = 76
   P [9261/8000 – 1 – 16/100] = 76
   
   
8. A sum of money is lent at simple interest and compound interest. The ratio between the difference of compound interest and simple interest of 3 years and 2 years is 35 : 11. What is the rate of interest per annum?
   A) 20 3/4%
   B) 17 2/5%
   C) 18 2/11%
   D) 22 1/5%
   E) 24 5/6%
   
   C) 18 2/11%
   Explanation:
   Difference in 3 yrs = Pr2(300+r)/1003
   Difference in 2 yrs = Pr2/1002
   So Pr2(300+r)/1003 / Pr2/1002 = 35/11 (300+r)/100 = 35/11
   
   
9. A sum of money borrowed at 5% compound interest is to paid in two annual installments of Rs 882 each. What is the sum borrowed?
   A) Rs 1650
   B) Rs 2340
   C) Rs 2630
   D) Rs 1640
   E) Rs 2640
   
   D) Rs 1640
   Explanation:
   P = 882/[1 + 5/100] + 882/[1 + 5/100]2
   
   
10. Rs 3903 is to be divided in a way that A’s share at the end of 7 years is equal to the B’s share at the end of 9 years. If the rate of interest is 4% compounded annually, find A’s share.
    A) Rs 2475
    B) Rs 1875
    C) Rs 2175
    D) Rs 1935
    E) Rs 2028
    
    B) Rs 1875
    Explanation:
    A’s share = (1 + 4/100)7
    B’s share = (1 + 4/100)9
    Divide both, B/A = (1 + 4/100)2 = 676/625
    So A’s share = 625/(676+625) * 3903