Question

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.
​

Answer 1

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