Calculate the amount and compound interest on
(a) ₹ 10,800 for 3 years at 12(1/2)% per annum compounded annually
(b) ₹ 18,000 for 2(1/2) years at 10% per annum compounded annually
(c) ₹ 62,500 for 1(1/2)years at 8% per annum compounded half yearly
(d) ₹ 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify)
(e) ₹ 10,000 for 1 year at 8% per annum compounded half yearly

Solution:

What is known: Principal, Time Period and Rate of Interest

What is unknown: Amount and Compound Interest (C.I)

Reasoning:

A = P[1+(r/100)]ⁿ

Steps:

(i)

P = ₹ 10800

N = 3 years

R = 12(1/2)% = (25/2)% compounded annually

A = P[1+(r/100)]ⁿ

A = 10800[1+(25/(2×100))]³

A = 10800 (225/200)³

A = 10800 × (225/200) × (225/200) × (225/200)

A = 15377.34

C.I. = A - P

= 15377.34 - 10800

= 4577.34

Answer: Amount = ₹ 15377.34

Compound Interest = ₹ 4577.34

(ii)

P = ₹ 18000

N = 2(1/2) years

R = 10% compounded annually

A = P[1+(r/100)]ⁿ

Since 'n' is 2(1/2) years, amount can be calculated for 2 years and having amount as principal Simple Interest(S.I.) can be calculated for 1/2 years because C.I. is only annually

A = P[1+(r/100)]ⁿ

A = 18000[1+(10/100)]²

A = 18000 × (11/10) × (11/10)

A = 21780

Amount after 2 years = ₹ 21870

S.I. for 1/2 years = 1/2 × 21780 × 10/100

= 1089

Amount after 2(1/2) years = 21780+1089

= ₹ 22869

C.I. after 2(1/2) years = 22869 - 18000

= ₹ 4869

Answer: Amount = ₹ 22869

Compound Interest = ₹ 4869

(iii)

P = ₹ 62,500

N = 1(1/2) years

R = 8% compounded half yearly

A = P[1+(r/100)]ⁿ

There are 3 half years in 1(1/2) years. Therefore, compounding has to be done 3 times and rate of interest will be 4%.

A = P[1+(r/100)]ⁿ

A = 62500[1+(4/(100)]³

A = 62500 (104/100)³

A = 62500 × (104/100) × (104/100) × (104/100)

A = 70304

C.I. = A - P

= 70304 - 62500

= 7804

Answer: Amount = ₹ 70304

Compound Interest = ₹ 7804

(iv)

P = ₹ 8000

n = 1 year

R = 9% p.a. compounded half yearly

A = P[1+(r/100)]ⁿ

S.I. for 1st 6 months = (1/2) × 8000 × (9/100)

= 40 × 9

= 360

Amount after 1^st 6 months including Simple Interest = 8000 + 360

= ₹ 8360

Principal for 2^nd 6 months = ₹ 8360

S.I. for 2^nd 6 months = 1/2 × 8360 × 9/100

= (418×9)/100

= 376.20

C.I. after 1 year (9% p.a. interest half yearly) = 360 + 376.20

= 736.20

Amount after 1 year (9% p.a. interest half yearly) = 8000 + 736.20

= 8736.20

Answer: Amount = ₹ 8736.20

Compound Interest = ₹ 736.20

(v)

P = ₹ 10,000

n = 1 year

R = 8% p.a. compounded half yearly

A = P[1+(r/100)]ⁿ

There are 2 half years in 1 years. Therefore, compounding has to be done 2 times and rate of interest will be 4%

A = P[1+(r/100)]ⁿ

A = 10000[1+(4/100)]²

A = 10000 × (104/100) × (104/100)

A = 10816

C.I. after 1 year (8% p.a. interest half yearly) = 10816 - 10000

= 816

Amount after 1 year (8% p.a. interest half yearly) 10816 = 10816

Answer: Amount after 1 year = ₹ 10816

Compound Interest after 1 year = ₹ 816

☛ Check: NCERT Solutions for Class 8 Maths Chapter 8

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Video Solution:

Calculate the amount and compound interest on(a) ₹ 10,800 for 3 years at 12(1/2)% per annum compounded annually(b) ₹ 18,000 for 2(1/2) years at 10% per annum compounded annually(c) ₹ 62,500 for 1(1/2)years at 8% per annum compounded half yearly(d) ₹ 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify)(e) ₹ 10,000 for 1 year at 8% per annum compounded half yearly

NCERT Solutions Class 8 Maths Chapter 8 Exercise 8.3 Question 1

The amount and compount interest are (i) ₹ 15377.34 and ₹ 4577.34 (ii) ₹ 22869 and ₹ 4869 (iii) ₹ 70304 and ₹ 7804 (iv) ₹ 8736.20 and ₹ 736.20 (v) ₹ 10816 and ₹ 816

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