Question

You have rs 1000 with 8% p.a compounded every 6 months. what is the total interest you get after 1 year.

Answer 1

Given that,
Principal, p = Rs 1000
Rate, r( p.a. )= 8% => r (half yearly )= 4%
Time,  t= 1 year 
since, it is compunded half yearly , n = 2
As we know,
Compound interest (CI) =  P{$(1+r/100)^{n}$-1}
Substituing P, r and n values in above formula:
CI = 1000{$(1+4/100)^{2}$-1}
     = 1000{$(104/100)^{2}$-1}
     = 1000{$(26/25)^{2}$-1}
     = 1000{$\frac{676}{625}$-1}
     = 1000{$\frac{676-625}{625}$}
     = 1000×$\frac{51}{625}$
     = 81.6
Hence, total interest after 1 year will be Rs 81.6

Answer 2

Solution -

Principal = Rs. 1000

Rate of interest = 8 % p.a.

As it is compounded half yearly then the interest rate = 4 %

And time = n = 2 (as there are two 6 months in a year)

A = 1000 × (1 + R/100)^n

= 1000 × (1 + 4/100)^2

= 1000 × 104/100 × 104/100

= 10816000/10000

A = Rs. 1081.6

Interest amount = 1081.6 - 1000

= Rs. 81.6

Total amount of interest is Rs. 81.60

Answer.