Question

Find total amount when $Rs.18,000$ for $2\frac{1}{2}$ years at $10\%$ per annum compounded annually.

Answer 1

Given:

Pricipal, $\left(P\right)=Rs.18,000$

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

Rate of interest $\left(R\right)=10\%$

Now, the total amount on compounded annually $\left(A\right)=?$

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

Since the time is $2\frac{1}{2}$ years.

So, first evaluate the total amount on compounded annually for $2$ years.

$\Rightarrow A=18000(1+\frac{10}{100}{)}^2$

$\Rightarrow A=18000(1+\frac{1}{10}{)}^2$

$\Rightarrow A=18000\times (\frac{11}{10}{)}^2$

$\Rightarrow A=18000\times \frac{11}{10}\times \frac{11}{10}$

$\Rightarrow A=180\times 11\times 11$

$\Rightarrow A=21780$

i.e., Total amount after two years is $Rs.21780$

It will become a new Principal based on compounded annually.

So, After two two years, $P_1=Rs.21780$

Remaining time $T=\frac{1}{2}$ year

Now, Interest for remaining half year,

$I=\frac{P_1\times T\times R}{100}$

$\Rightarrow I=\frac{Rs.21780\times 1\times 10}{2\times 100}$

$\Rightarrow I=Rs.1089$

Therefore, Total amount in $2\frac{1}{2}$ years,

$A_1=P_1+I$

$\Rightarrow A_1=Rs.21780+Rs.1089$

$\Rightarrow A_1=Rs.22869$

Hence, the required amount is $Rs.22,869$.