NCERT Solutions
Class 8 Maths
Comparing Quantities
Ex.8.3 Q.1
Calculate the amount and compound interest on:
(a) Rs 10,800 for 3 years at 1212
% per annum compounded annually.
(b) Rs 18,000 for 212 years at 10% per annum compounded annually.
(c) Rs 62,500 for 112 years at 8% per annum compounded annually.
(d) Rs 8,000 for 1 years at 9% per annum compounded half yearly.
(You could the year-by-year calculation using S.I. formula to verify).
(e) Rs 10,000 for 1 years at 8% per annum compounded half yearly.
(a) Here, Principal (P) = Rs 10800, Time (n) = 3 years
Rate of interest (R) = 12
% = 
%
Now, amount (A) = P (1 + 
) n
= 10800{1 + (25 ÷ (2 × 100))}3
= 10800{1 + (1 ÷ (2 × 4))}3
= 10800(1 + (1 ÷ 8))3
= 10800 (9 ÷ 8)3
= 10800 × 
× ×
= 1350 × 9 × ×
= (1350 × 9 × 9 × 9) ÷ 64
= 109350 ÷ 64
= Rs15377.34
Compound Interest (C.I.) = A – P = Rs 10800 – Rs 15377.34 = Rs 4,577.34
(b) Here, Principal (P) = Rs 18000, Time (n) = 2 years
Rate of interest (R) = 10 %
Now, amount (A) = P (1 + 
)n
= 18000(1 + 
)2
= 18000(1 + 
)2
= 18000(
)2
= 18000 × ×
= Rs 21780
Interest for years on Rs 21,780 at rate of 10% = ( ) × (21780 × 10 × 1) ÷ 100
= Rs 1,089
Total amount for years = Rs 21,780 + Rs 1089 = Rs 22,869
Compound Interest (C.I.) = A – P = Rs 22869 – Rs 18000 = Rs 4,869
(c) Principal (P) = Rs 62500, Time (n) = 1 = 
years
= 3 half-years (compounded half yearly)
Rate of interest (R) = 8% = 4% (compounded half yearly)
Now, amount (A) = P (1 + )n
= 62500(1 + 
)3
= 62500(1 + 
)3
= 62500(
)3
= 18000 × × ×
= Rs70304
Compound Interest (C.I.) = A – P = Rs 70304 – Rs 62500 = Rs 7,804
(d) Principal (P) = Rs 8000, Time (n) = 1 years = 2 half-years (compounded half yearly)
Rate of interest (R) = 9% = 9/2 % (compounded half yearly)
Now, amount (A) = P (1 + )n
= 8000{1 + (9 ÷ (2 × 100))}2
= 10800{1 + (9 ÷ 200)}2
= 8000(209 ÷ 200)2
= 8000 × 
×
= Rs 8,736.20
Compound Interest (C.I.) = A – P = Rs 8736.20 – Rs 8000 = Rs 736.20
(e) Principal (P) = Rs 10,000, Time (n) = 1 years = 2 half-years (compounded half yearly)
Rate of interest (R) = 8% = 4% (compounded half yearly)
Now, amount (A) = P (1 + )n
= 10000(1 + )2
= 10000(1 + )2
= 10000( )2
= 10000 × ×
= Rs 10,816
Compound Interest (C.I.) = A – P = Rs 10,816 – Rs 10,000 = Rs 816