1. The simple interest on some principal at some rate for 3 years is 525. At thesame rate, the compound interest on 1600 for 2 years is 164. What is theprincipal?(1) * 4500(2) 3500(3) 3000(4) * 4000 About the author Serenity
Answer: Here is your answer R = 3 years SI = Rs 525 Let rate of interest= R and principal be x Now SI = PRT/100 \begin{gathered}525 = \frac{x \times r \times 3}{100} \\ r = \frac{525 \times 100}{3x} \\ r = \frac{17500}{x} \%\end{gathered} 525= 100 x×r×3 r= 3x 525×100 r= x 17500 % Hence For Compound Interest T = 2 years P = Rs 1600 CI = 164 R = 17500/x % A = 1600 + 164 = Rs 1764 As we know the formula A = P{1+R/100)^t \begin{gathered}1764 = 1600(1 + \frac{17500}{x \times 100} ) {}^{2} \\ \frac{1764}{1600} = (1 + \frac{175}{x} ) {}^{2} \\ \frac{441}{400} = (1 + \frac{175}{x} ) {}^{2} \\ ( \frac{21}{20} ) {}^{2} = (1 + \frac{175}{x} ) {}^{2} \\ on \: comparing \\ \frac{21}{20} = 1 + \frac{175}{x} \\ \frac{21}{20} – 1 = \frac{175}{x} \\ \frac{21 – 20}{20} = \frac{175}{x} \\ \frac{1}{20} = \frac{175}{x} \\ x = 175 \times 20 \\ x = 3500\end{gathered} 1764=1600(1+ x×100 17500 ) 2 1600 1764 =(1+ x 175 ) 2 400 441 =(1+ x 175 ) 2 ( 20 21 ) 2 =(1+ x 175 ) 2 oncomparing 20 21 =1+ x 175 20 21 −1= x 175 20 21−20 = x 175 20 1 = x 175 x=175×20 x=3500 Therefore Principal is Rs 3,500 Reply
Answer:
Here is your answer
R = 3 years
SI = Rs 525
Let rate of interest= R and principal be x
Now
SI = PRT/100
\begin{gathered}525 = \frac{x \times r \times 3}{100} \\ r = \frac{525 \times 100}{3x} \\ r = \frac{17500}{x} \%\end{gathered}
525=
100
x×r×3
r=
3x
525×100
r=
x
17500
%
Hence For Compound Interest
T = 2 years
P = Rs 1600
CI = 164
R = 17500/x %
A = 1600 + 164 = Rs 1764
As we know the formula
A = P{1+R/100)^t
\begin{gathered}1764 = 1600(1 + \frac{17500}{x \times 100} ) {}^{2} \\ \frac{1764}{1600} = (1 + \frac{175}{x} ) {}^{2} \\ \frac{441}{400} = (1 + \frac{175}{x} ) {}^{2} \\ ( \frac{21}{20} ) {}^{2} = (1 + \frac{175}{x} ) {}^{2} \\ on \: comparing \\ \frac{21}{20} = 1 + \frac{175}{x} \\ \frac{21}{20} – 1 = \frac{175}{x} \\ \frac{21 – 20}{20} = \frac{175}{x} \\ \frac{1}{20} = \frac{175}{x} \\ x = 175 \times 20 \\ x = 3500\end{gathered}
1764=1600(1+
x×100
17500
)
2
1600
1764
=(1+
x
175
)
2
400
441
=(1+
x
175
)
2
(
20
21
)
2
=(1+
x
175
)
2
oncomparing
20
21
=1+
x
175
20
21
−1=
x
175
20
21−20
=
x
175
20
1
=
x
175
x=175×20
x=3500
Therefore
Principal is Rs 3,500