4. Find the rate of compound interest on
(i) Rs 6,500 so that it can amount to Rs 7,865 in 2 years
(ii) Rs 4,000 so that it can amount to Rs 4,630.50 in 3 years
Answers
Answer:1. rate of interest is 10% p.a.
2.rate of interest is 5% p.a.
Step-by-step explanation:1.
p =6500
a=7865
n=2yrs
7865 = 6500(1+r/100)²
1573 = 1300(1+r/100)²
121 = 100(1+r/100)²
121/100 = (1+r/100)²
√121/100 = 1+r/100
11/10 =100+r/100
11 = 100+r/10
110 = 100+r
110-100 = r
10 = r
2.
p= 4000
a= 4360.50
n=3yrs
4630.50 = 4000(1+r/100)³
1157.625 = 1000(1+r/100)³
1157.625/1000 = (1+r/100)³
∛1157.625/1000 = 1+r/100
10.5/10 =1+r/100
10.5 = 100+r/10
105 = 100+r
105-100 = r
5 = r
please mark me brainlist???
1) 10 %
2) 5%
Step-by-step explanation:
1) Here P = ₹ 6500
A = ₹ 7865
n = 2 years
A = P ( 1 + r / 100 ) n
7865 = 6500 ( 1 + r / 100 ) 2
7865 / 6500 = ( 1 + r / 100 ) 2
1.21 = ( 1 + r/ 100 ) 2
Taking square root both side,
we get,
1.1 = 100 + r / 100
11/ 10 = 100 + r / 100
11 = 100 + r / 10
11 × 10 = 100 + r
110 = 100 + r
110 - 100 = r
10 = r
The rate is 10 %
b)
Here P = 4000
A = 4630.50
n = 3 years
A = P × ( 1 + r / 100 ) ^n
4630.50 = 4000 ( 1 + r / 100 ) ^ 3
4630.50 / 4000 = ( 1 + r / 100 ) ^ 3
4630.50 × 100 / 4000 × 100 = ( 1+r/ 100 ) ^ 3 ( don't be confused here we multiply 100 to both the numbers for became calculation easiest)
463050 / 400000 = ( 1 + r / 100 ) ^ 3
9261 / 8000 = ( 1 + r / 100 ) ^ 3
Taking cubic root both side,
we get
(21 / 20) ^ 3 =( 1 + r/ 100 ) ^ 3 ( cubic roots cancel out then we get)
21/ 20 = 1 + r / 100
21 / 20 - 1 = r / 100
21- 20/ 20 = r / 100
1/ 20 = r / 100
1× 100/ 20 = r
100/ 20 = r
5 = r
so, the rate is 5 %
The solution of these questions too long but it's ok
Hope it helps you