# 6  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.

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

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