Question

calculate the amount and compound interest on ₹18,000 for 3/2 years at 10% per annum compounded annually​

Answer 1

$\bf{\huge{\boxed{\underline{\mathfrak{\red{Answer:}}}}}}$

Principal = Rs18,000

Time (n) = $\frac{3}{2}$ years = 1$\frac{1}{2}$

Rate =10 $\%$

Since time is in fraction, we will solve it by :

$\star$ Finding Compound Interest for 1 years + Simple Interest of $\frac{1}{2}$years

$\textbf{\underline{\underline{Compound\:Interest\:For\:1\:Years}}}$

Principal = Rs18,000

Time = 1 years

Rate = 10$\%$

Amount = P(1+$\frac{r}{100})^n$

$\implies$ 18,000(1+$\frac{10}{100})^1$

$\implies$18,000 × $\frac{11}{10}$

$\huge{\boxed{Rs\:19800}}$

Since,

$\implies$ Amount = Principal + Interest

$\implies$ 19800 = 18000 + Interest

$\implies$ 19800 -18000 = Interest

$\implies$ 1800= Interest

$\therefore$Interest for 2 years = Rs1800

$&$ Amount for 2 years = Rs 19800

$\textbf{\underline{\underline{Simple\:Interest\:For\:next\:1/2 \:Years}}}$

Amount will be Principal after 1 year

P = Rs 19800

R =10 $\%$

T = $\frac{1}{2}$years

Interest = $\dfrac{P\:\times\:R\:\times\:T}{100}$

$\implies\:\dfrac{19800\:\times\:10\:\times\:1}{100\:\times\:2}$

$\huge{\boxed{Rs\:990}}$

$\therefore$Simple Interest for $\frac{1}{2}$years = Rs 990

Now,

Interest for 1$\frac{1}{2}$years =

$\implies$ Compound Interest for 1 year + Simple Interest of $\frac{1}{2}$years

$\implies$Rs 19800 + Rs 990

$\huge{\boxed{Rs\:20,790}}$

Amount = Principal + Interest

Amount = Rs 18000 + Rs 20,790

$\huge{\boxed{Rs\:38790}}$

Thus,

Interest = Rs 20,790

Amount = Rs 38790