. The difference between the compound interest and the simple interest on a certain sum for
2 years at 6% per annum is * 90. Find the sum.
Answers
Answer:
C.I.−S.I.=18
(P(1+
100
R
)
n
−P)−(
100
P×R×n
)=18
Given:-
P=?
R=6%
n=2 years
P(1+
100
6
)
2
−P−
100
P×6×2
=18
P(
100
106
)
2
−P−
25
3P
=18
1.1236P−P−0.12P=18
0.0036P=18
P=
0.0036
18
=5000
Answered By
Answer:
25000.
Step-by-step explanation:
Given:
Interest rate =6% per annum
Time =2 years
Simple interest (SI)=PTR/100
where P is principle amount, T is time taken, R is rate per annum
Let sum is P
Now,
SI=(P×2×6)/100
⇒SI=(12P)/100
⇒SI=(3P)/25 —————- equation 1
To find the amount we have the formula,
Amount (A)=P(1+(r/100))n
where P is present value, r is rate of interest, n is time in years.
Also, CI=A−P
Now substituting the values in above formula we get,
∴CI=P(1+6/100)² −P
⇒CI=P(1+3/50)² −P
⇒CI=P(53/50)² −P
⇒CI=P(2809)/(2500)–P
⇒CI=309P/2500 ——– equation 2
Now the difference is
(CI–SI)=309P/2500–(3P)/25
⇒90=309P/2500–(3P)/25
⇒90=309P–(300P)/2500
⇒90=9P/2500
⇒P=90×2500/9
⇒P=10×2500
⇒P=25000
∴ Sum =25000