Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after  1\frac{1}{2}   years if the interest is-

   (i) compounded annually.  

   (ii) compounded half yearly.

Answers (1)
H Harsh Kankaria

(i) Given,

Principal amount, P = Rs 80000

Rate of interest, R = 10% p.a.

Time period = 1\frac{1}{2} years.

We know, Amount when interest is compounded annually, A =

A =P(1+\frac{R}{100})^n

Now, For the first year, A=

          A =80000(1+\frac{10}{100})^1= Rs. 88000

For the next half year, this will act as the principal amount.

\therefore Interest for 1/2 year at 10% p.a = 

              =\frac{88000\times\frac{1}{2}\times10}{100}= Rs 4400 

Required total amount = Rs (88000 + 4400) = Rs 92400

(ii) If it is compounded half yearly, then there are 3 half years in 1\frac{1}{2} years.

       \therefore n = 3 half years.

And, Rate of interest = half of 10% p.a = 5% half yearly

 \therefore A =80000(1+\frac{5}{100})^3= Rs.\: 92610 

 \therefore The difference in the two amounts = Rs (92610 - 92400) = Rs 210