Question

Question 8
Find the amount and the compound interest on Rs 10,000 for 10,000 for $1\frac{1}{2}$years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

Answer 1

Here, Principal (P) = Rs 10000 Rate of interest (R) = 10% = 5% (Compounded half yearly)
Time (n) = $1\frac{1}{2}$ years = 3 years (compounded half yearly)
$Amount\left(A\right)=P{(1+\frac{R}{100})}^n=10000{(1+\frac{5}{100})}^3=10000{(1+\frac{1}{20})}^3$
$=10000{\left(\frac{21}{20}\right)}^3=10000\times \frac{21}{20}\times \frac{21}{20}\times \frac{21}{20}$
=Rs 11,576.25
Compound Interest (C.I)=Rs 10000, Rate of interest (R) = 10% Time (n) = 1 years
Amount (A) for 1 year = $P{(1+\frac{R}{100})}^n=10000{(1+\frac{10}{100})}^1=10000{(1+\frac{1}{10})}^1$
$=10000{\left(\frac{11}{10}\right)}^1=10000\times \frac{11}{10}$
=Rs 11,000
Interest for year $=\frac{1}{2}year=\frac{11000\times 1\times 10}{2\times 100}Rs.550$
$\therefore$ Total amount = Rs 11,000 + Rs 550 = Rs 11,550
Now, C.I = A - P = Rs 11,550 - Rs 10000 = Rs 1550
Yes interest Rs 1576.25 is more than Rs 1550.