The compound interest of a sum of money in 2 years and 4 years are Rs 1050 and Rs 2320.50 respectively. Find the rate of interest compounded yearly and the principal.
Answers
Answer:
Step-by-step explanation:
simple Interest, S.I. = Rs. 1260 =
100
PR×2
=
50
PR
-(i)
Compound Interest, C.I. = Amount(A) - Principle(P)
=P(1+
100
R
)
2
- P = PR(R/10000+1/50)=Rs.1323 -(ii)
Dividing (ii) by (I),
200
R
+1 =
1260
1323
⇒Rate,R=10%p.a.
Now,
100
PRT
=1260
⇒
100
P×10×2
=1260
⇒ Principal or Sum , P = Rs.6,300
OR
Let the sum of money be
′
x
′
.
T=2 years
C.I=2700. , Rate=R
A=P(1+
100
R
)
2
⇒
(x+2700)=x(1+
100
R
)
2
⟶(I)
Now,
S.I=2500
⇒2500=
100
x×R×2
⇒
xR=125000
⇒
R=
x
125000
→(II)
Putting
′
x
′
in eq (I)
(
R
125000
+2700)=
R
125000
(1+
100
R
)
2
⇒(
R
125000+2700R
)=
R
125000
(1+
100
R
)
2
⇒(125000+2700R)=125000(1+
100
R
)
2
⇒1250+27R=1250(1+
100
R
)
2
⇒1250+27R=1250(1+2(0.0R)+(0.0R)
2
)
⇒1250+27R=1250+25R+0.125R
2
⇒0.125R
2
−2R=0
⇒R(0.125R−2)=0
⇒R=0 or 0.125R−2=0
But R can't be 0.
∴0.125R−2=0
⇒R=
0.125
2
=16
∴
R=16
S