Chapter 14: Compound Interest - KopyKitab

Exercise 14.1

Chapter 14: Compound Interest

Q1) Find the compound interest when principal = Rs 3000, rate = 5% per annum and tim e = 2 years.

Solution: Principal for the first year = Rs 3,000 Interest for the first year=Rs3,000 x 5 x ^ = Rs 150 Am ount at the end of the first year = Rs 3,000 + Rs 150 = Rs 3,150

Principle Interest for the second year=Rs 3,150 x 5 x 4 = Rs 157.50 Amount at the end of the second year = Rs 3307.50 Compound interest=Rs 3,307.50 - 3,000 = Rs 307.50

Q2) What will be the compound interest on Rs 4000 in two years when the rate o f interest is 5% per annum?

Solution: W e know that am ount A at the end of n years at the rate of R% per annum is given by A = P(1 + 4 ) " Giver P = Rs 4,000 R = 5% p.a n = 2 years Now, A =4 0 0 0 (l+ 4 )2 =4 0 0 0 (4 )2 = Rs 4410 And, Cl = A - P = Rs 4,410 - Rs 4,000 = Rs 410

Q3) Roh'rt deposited Rs 8000 with a finance company for 3 years at an interest o f 15% per annum. What is the compound interest that Rohit gets after 3 years?

Solution: W e know that am ount A at the end of n years at the rate of R% per annum is given by = A = P ( 1 + 4 ) n Given: P = Rs 8,000 R = 15% p.a. n = 3 years. Now, A =8 0 0 0 (l+ 4 )3 A =8 0 0 0 (4 )3 A = Rs. 12,167 And, Cl = A - P = Rs 12,167 - Rs 8,000 = Rs 4,167

Q4) Find the compound interest on Rs 1000 at the rate of 8% per annum for 1 j years when interest is compounded half-yearly.

Solution: Given: P = Rs 1,000 R = 8% p.a. n = 1.5 years We know that: A = - P ( l + 4 ) 2n A = 1000(1+ 4 ) 3 A = 1 0 0 0 (4 )2 A = Rs 1,124.86 Now, Cl = A - P = Rs 1,124.86 - Rs 1,000 = Rs 124.86

Q5) Find the compound interest on Rs 160000 for one year at the rate o f 20% per annum, if the interest is compounded quarterly.

Solution: Given: P = Rs 160,000 R = 20 % p. a. n = 1 year We know that: a =-P(i + 4 ^ ) 4" A = 160000(1+ ^ ) 4 A = 160000(1.05)4 A = Rs 19,4481 Now, Cl = A - P = Rs 19,448.1 - Rs 16,000 = Rs 3,4481

Q6) Swat! took a loan of Rs 16000 against her insurance policy at the rate of 121% per annum. Calculate the total compound interest payable by Swati after 3 year.

Solution: Given: P = 16,000 R = 12.5% p.a. n = 3 years We know that: A = -P (i + i? r)n A = 16000(1 + ^ ) 3 a =1 6 0 0 0 (^ )3 A = Rs 22,781.25 Now, Cl = A - P = Rs 22,781.25 - Rs 16,000 = Rs 6,781.25

Q7) Roma borrowed Rs 64000 from a bank for 1 j years at the rate of 10% per annum. Compute the total compound interest payable by Roma after 1 j years, if the interest is compounded half-yearly.

Solution: Given: P = 64,000 R = 10% p.a. n = 1.5 years Amount after n years: a =-P(i + 4 ) 2" A = 64000(1 + ^ ) 3 A = 6 4 0 0 0 (?? )3 A = Rs 74,088 Now, Cl = A - P = Rs 74,088 - Rs 64,000 = Rs 10,088

Q8) Mewa Lai borrowed Rs 20000 from his friend Rooplal at 18% per annum simple interest. He lent it to Rampal at the same rate but compounded annually. Find his gain after 2 years.

Solution: SI for M ew a Lai = 4 ^ = 20QQ? ^ 8x21 = Rs 7,200 Thus, he has to pay Rs 7,200 as interest after borrowing Cl for M ew a Lai = A - P = 2 0 0 0 0 (1 + ^ ) 2 - 20,000 = 2 0 0 0 0 (1 .1 8 )2 - 20,000 = 27,848- 20,000 = Rs 7,848 He gained Rs 7,848 as interest after lending. His gain in the whole transaction = Rs 7,848 - Rs 7,200 = Rs 648

Q9) Find the compound interest on Rs 8000 for 9 months at 20% per annum compounded quarterly.

Solution: P = Rs 8,000 T = 9 months = 3 quarters R = 20% per annum = 5% per quarter A = 8000(1 + 4 ) 3 A = 8000(1.05)3 A = 9,261 The required am ount is Rs 9,261. Now, Cl = A - P = Rs 9,261 - Rs 8,000 = Rs 1,261

Q10) Find the compound interest at the rate of 10% per annum for two years on that principle which in two years at the rate o f 10% per annum gives Rs 200 as simple interest.

Solution:

Cl - P R r b l " too

.

51x100

" ^ - RT

r _ 200x100 ^ - 10x2

P = Rs 1,000

A = P (1 + ^ ) " A = 1000(1+ ^ ) 2 A = 1000(1.1)2 A = Rs 1,210 Now, Cl = A - P = Rs 1,210 - Rs 1,000 = Rs 210

Q11) Find the compound interest on Rs 64000 for 1 year at the rate of 10% per compounded quarterly.

Solution: To calculate the interest compounded quarterly.

W e have: a = - P ( 1 + 4 ^ ) 4" A = 64000(1 + ^ ) 4xl A = 64000(1.025)4 A = 70,644.03 Thus, The required am ount is Rs 70,644.03. Now, Cl = A - P = Rs 70,644.025 - Rs 64,000 = Rs 6,644.03

Q12) Ramesh deposited Rs 7500 in a bank which pays him 12% interest per annum compounded quarterly. What is the amount which he receives after 9 months?

Solution: Given: P = Rs 7,500 R = 12% p.a = 3% quarterly T = 9 months = 3 quarters We know that: A = -P(1 + m )" A = 7500(1+ 4 ) 3 A = 7500(1.03)3 A = 8,195.45 Thus, The required am ount is Rs 8,195.45.

Q13) Anil borrowed a sum of Rs 9600 to install a hand pump in his dairy. If the rate o f 1 interest is 5^% per annum compounded annually, determine the compound interest which Anil will have to pay after 3 years.

Solution: A = -P (l + w ) " A = 9600(1+ ^ ) 3 A = 9600(1.055)3 A = Rs 11,272.72 Now, Cl = A - P = Rs 11,272.72 - Rs 9,600 = Rs 1,672.72

Q14 ) Surabhi borrowed a sum of Rs 12000 from a finance company to purchase a refrigerator. If the rate of interest is 5% per annum compounded annually, calculate the compound interest that Surabhi has to pay to the company after 3 years.

Solution: a ^ U + tD '1 A = 12000(1+ ^ ) 3 A = 12000(1.0 5 )3 A = Rs 13,891.50 Thus, The required am ount is Rs 13.891.50.

Now, Cl = A - P = Rs 13.891.50 - Rs 12,000 = Rs 1,891.50

Q15) Dalj'rt received a sum of Rs. 40000 as a loan from a finance company. If the rate o f interest is 7% per annum com compounded annually, calculate the compound interest that Daljit pays after 2 years.

Solution: A=P( i + ^ r A = 4 0 0 0 0 (1 + -jgo ) 2 A = 40000(1.0 7 )2 A = Rs 4 5,796 Thus, The required am ount is Rs 45,796. Now, Cl = A - P = Rs 4 5 .7 9 6 - Rs 40,000 = Rs 5,796

Exercise 14.2

Chapter 14: Compound Interest

Q1) Compute the am ount and the compound interest in each of the following by using the form ulae when:

(i) Principal = Rs 3000, Rate = 5%, Tim e = 2 years

(ii) Principal = Rs 3000, Rate =18%, Tim e = 2 years

(iii) Principal = Rs 5000, Rate = 10 paise per rupee per annum. Tim e = 2 years

(iv) Principal = Rs 2000, Rate = 4 paise per rupee per annum. Tim e = 3 years

(v) Principal = Rs 12800, Rate = 7-|% , Tim e = 3 years

(vi) Principal =Rs 10000, Rate 20% per annum compounded half-yearly. Tim e = 2 years

(vii) Principal = Rs 160000, Rate =10 paise per rupee per annum compounded half-yearly. Tim e = 2 years.

Solution: Applying the rule A = P( 1 +

on the given situations, w e get:

(i) A = 3 0 0 0 (1 + iso ) 2 = 3 0 0 0 ( 1 .0 5 ) 2 = Rs 3307.5 Now, Cl = A - P = Rs 3307.50 - Rs 3000 = Rs. 307.50 (ii) A = 3 0 0 0 (1 + - ^ ) 2 = 3 0 0 0 (1 .1 8 )2 = Rs 4177.2 Now, Cl = A - P = Rs 417 7 .2 0 - Rs 3000 = Rs. 1177.20 (iii) A = 5 0 0 0 (1 + ^ ) 2 = 5 0 0 0 (1 .1 0 )2 = Rs 6050 Now, Cl = A - P = Rs 6050 - Rs 5000 = Rs. 1050 (iv) A = 2 0 0 0 (1 + ) 3 = 2 0 0 0 (1 .0 4 )3 = Rs 2249.68 Now, Cl = A - P = Rs 2249.68 - Rs 2000 = Rs. 249.68 (v) A = 1 2 8 0 0 (1 + ^ ? ) 3 = 1 2 8 0 0 (1 .0 7 5 )3 = Rs 15901.40 Now, Cl = A - P = Rs 15901.40 - Rs 12800 = Rs. 3 101.40 (vi) A = 1 0 0 0 0 (1 + ^ ) 4 = lO O O O (l.l)4 = Rs 14641 Now, Cl = A - P = Rs 14641 - Rs 10000 = Rs. 4641 (vii) A = 1 6 0 0 0 0 (1 + ^ ) 4 = 1 6 0 0 0 0 (1 .0 5 )4 = Rs 194481 Now, Cl = A - P = Rs 194481 - Rs 160000 = Rs. 34481 Q2) Find the am ount of Rs 2400 after 3 years, when the interest is compounded annually at the rate of 20% per annum. Solution: Given: P = Rs 2400 R = 20 % p.a n = 3 years W e know that am ount A at the end of n years at the rate R% per annum when the interest is compounded annually is given by

A = P (1 + ^ ) " A = 2400(1+ ^ ) 3 A = 2400(1.2 )3 A = 4147.20 Thus, the required am ount is Rs 4 147.20.

Q3) Rahman lent Rs 16000 to Rasheed at the rate of 1 2 -|% per annum compound interest. Find the amount payable by Rasheed to Rahman after 3 years. Solution: Given: P = Rs 16000 R = 12.5% p.a n = 3 years W e know that am ount A at the end of n years at the rate R% per annum when the interest is compounded annually is given by

A = -P (l + O T )n A = 16000(1+ ^ ) 3 A = 16000(1.125)3 A = 22781.25 Thus, the required am ount is Rs 22781.25. Q4) Meera borrowed a sum of Rs 1000 from Sita for tw o years. If the rate of interest is 10% compounded annually, find the am ount that Meera has to pay back. Solution:

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