# Simple interest on a sum for 2 yrs at 10% p.a is 1000. If the same amount is borrowed for 2 yrs at 8% p.a., compounded annually find the compound interest and amount to be paid after 2 yrs.

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The simple interest on a sum for 2 years at 10% p.a is 1000. If the amount borrowed is P, P*(0.1)*2 = 1000

=> P = `1000/(2*0.1) = 1000/0.2 = 5000`

If the same amount is borrowed at an interest rate of 8% per annum compounded annually, the interest incurred is `5000*((1 + 0.08)^2 - 1)` = 832. The amount to be repaid after 2 years is 5000 + 832 = 5832.

**The compound interest incurred is 832 and a total amount equal to 5832 has to be repaid after 2 years.**

given :

Simple Interest (SI)= 1000, Rate(R)=10% p.a. , Time(T)=2yrs.

We know that SI=(P*R*T)/100 [ where P=Principle ]

Or, P=(100*SI)/(R*T)

=> P= (100*1000)/(10*2) = 5000

now The the same amount i.e 5000 is borrowed for 2 yrs. at 8%p.a.

which is compounded annually i.e. as compound interest.

Using formula for compound interest :

Amount(A)= P(1+R/100)^T

A=5000(1+8/100)^2

=> A=5000(108/100)^2

=> A=5000(27/25)^2=(5000*27*27)/(25*25)

=> A=8*27*27= 5832

Hence Amount(A)=5832

Compound Interest(CI)= A-P= 5832-5000-832

Hence ,

**Amount to be paid =5832 ** And

**Compound Interest = 832**