annually?
19 At what rate per cent per annum will 640 amount to * 774.40 in 2 years when
compounded annually?
20. In how
when compounded
Answers
Answer:
Here is your answer,
Principal (P) = Rs. 640
Rate of interest (R) = R%
Time (n) = 2 years
Amount = Rs. 774.40
\begin{gathered}Amount = P {(1 + \frac{R}{100} )}^{n} \\ \\ = > 774.40 = 640 {(1 + \frac{R}{100} )}^{2} \\ \\ = > \frac{77440}{100} = 640 {(1 + \frac{R}{100} )}^{2} \\ \\ = > \frac{7744}{10} = 640 {(1 + \frac{R}{100} )}^{2} \\ \\ = > \frac{7744}{10} \div 640 = {(1 + \frac{R}{100} )}^{2} \\ \\ = > \frac{7744}{10} \times \frac{1}{640} = {(1 + \frac{R}{100} )}^{2} \\ \\ = > \frac{7744}{6400} = {(1 + \frac{R}{100} )}^{2} \\ \\ (7744 = {88}^{2} \: \: and \: \: 6400 = {80}^{2} ) \\ \\ = > ({ \frac{88}{80} )}^{2} = {(1 + \frac{R}{100} )}^{2} \\ \\ = > \frac{88}{80 } = 1 + \frac{R}{100} \\ \\ = > \frac{88}{80} - 1 \: \: = \: \: \frac{R}{100} \\ \\ = > \frac{88 - 80}{80} = \frac{R}{100} \\ \\ = > \frac{8}{80} = \frac{R}{100} \\ \\ = > \frac{8}{80} \times 100 = R \\ \\ = > \frac{800}{80} = R \\ \\ = > 10 = R \\ \end{gathered}
Amount=P(1+
100
R
)
n
=>774.40=640(1+
100
R
)
2
=>
100
77440
=640(1+
100
R
)
2
=>
10
7744
=640(1+
100
R
)
2
=>
10
7744
÷640=(1+
100
R
)
2
=>
10
7744
×
640
1
=(1+
100
R
)
2
=>
6400
7744
=(1+
100
R
)
2
(7744=88
2
and6400=80
2
)
=>(
80
88
)
2
=(1+
100
R
)
2
=>
80
88
=1+
100
R
=>
80
88
−1=
100
R
=>
80
88−80
=
100
R
=>
80
8
=
100
R
=>
80
8
×100=R
=>
80
800
=R
=>10=R