Question

Arif took a loan of Rs. $80,000$ from a bank. If the rate of interest is $10$% p.a., find the difference in amounts he would be paying after $1\frac{1}{2}$ years if the interest is (i) compounded annually and (ii) compounded half-yearly.

Answer 1

1) Compounded Annually :

$P=Rs.80000$

$R=10$% $p.a.$

$T=1\frac{1}{2}$ years $⟹n=1+\frac{1}{2}$

Amount for 1st year.

$A=P[1+\frac{R}{100}{]}^n$

$=Rs.80000[1+\frac{10}{100}]=Rs.88000$

SI on Rs. 88000 for next 1/2 year

$=Rs.88000\times \frac{10}{100}\times \frac{1}{2}=Rs.4400$

Therefore, Amount = $Rs.88000+Rs.4400$ = $92400Rs.$

2) Compounded half yearly :

$P=Rs.80000$

$R=10$% $p.a.=5$% per half year

$T=1\frac{1}{2}$ years $⟹n=3$

$A=Rs.80000[1+\frac{5}{100}{]}^3$

$A=Rs.92610$

Thus, the difference between the two amounts = $Rs.92610-Rs.92400$ =$Rs.210$