If a sum becomes Rs. 6,655 in 3 years and Rs. 7,320 in 4 years interest being compounded annually, find the rate of interest and the sum .
Answers
Let the initial amount of money be P.
A=P(1+ 100 R )T
Rate of Interest :
where R= Rate of Interest and T= Time period.
Amount after 3 years =6500
⇒6500=P(1+ 100 R ) 3 ⟶(I)
Amount :
Amount after 6 years =10,562.5
⇒10562.5=P(1+ 100 R ) 6 ⟶(II) From eq(I),
P 6500 =(1+ 100 R ) ³
⇒( P 6500 ) ² =(1+ 100 R )
Step by step explanation :
⟶(III) Putting eq(III) in eq(II)
10562.5=P( P 6500 ) ²
⇒10562.5=P× P 2 (6500) ²
⇒P= 10562.5 (6500) ² =4000
Hence, the initial amount of money is equal to Rs. 4000.
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Step-by-step explanation:
Let the initial amount of money be P.
A=P(1+
100
R
)
T
where R= Rate of Interest and T= Time period.
Amount after 3 years =6500
⇒6500=P(1+
100
R
)
3
⟶(I)
Amount after 6 years =10,562.5
⇒10562.5=P(1+
100
R
)
6
⟶(II)
From eq(I),
P
6500
=(1+
100
R
)
3
⇒(
P
6500
)
2
=(1+
100
R
)
6
⟶(III)
Putting eq(III) in eq(II)
10562.5=P(
P
6500
)
2
⇒10562.5=P×
P
2
(6500)
2
⇒P=
10562.5
(6500)
2
=4000
Hence, the initial amount of money is equal to Rs. 4000.