the difference between the compound intrest and simple intrest for 2 years at 10% per annum is 90. find the sum
Answers
Answer:
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
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 pls