Question

Calculate the amount and compound interest on
(a) $Rs10,800$ for $3$ years at $12\frac{1}{2}$% per annum compounded annually.
(b)$Rs18,000$ for $2\frac{1}{2}$ years at $10$% per annum compounded annually.
(c)$Rs62,500$ for $1\frac{1}{2}$ years at $8$% per annum compounded annually.
(d)$Rs8,000$ for $1$ years at $9$% per annum compounded annually.
(e)$Rs10,000$ for $1$ years at $8$% per annum compounded annually.

Answer 1

(a)
$\text{Principal}\left(p\right)=Rs10,800$
$\text{Rate(R)}=12\frac{1}{2}\text{\%}=\frac{25}{2}\text{\% per annum}$
Time of years = 3 years
$\therefore \text{Amount}\left(A\right)=P({(1+\frac{R}{100})}^n$
$\Rightarrow A=[10,800\times {(1+\frac{25}{200})}^3]$
$\Rightarrow A=[10,800\times {\left(\frac{225}{200}\right)}^3]=15,377.34375$
$\Rightarrow A=Rs15,377.34\text{(approximately)}$

$C.I=\text{Amount-Principle}$
$C.I=Rs\mathrm{15.377.34}-Rs10,800$
$C.I=Rs4,577.34$\

(b)
Given$\text{Principal (P) = ₹18,000}$
$\text{Rate(R)=10\% per annum}$
$\text{Time of years}=2\frac{1}{2}years$

First, we calculate the amount for 2 years using the compound interest formula
after that calculate amount for 6 months using the simple interest formula.
Amount for 2 years,
$\therefore \text{Amount}\left(A\right)=P({(1+\frac{R}{100})}^n$

$\Rightarrow A=[18,000\times {(1+\frac{1}{10})}^2]$

$\Rightarrow A=[18,000\times {\left(\frac{11}{10}\right)}^2]$

$\Rightarrow A=Rs21,780$

Calculate the interest for $\frac{1}{2}$ year.
By taking Rupees $Rs21,780$ as principal, the S.I. for the next $\frac{1}{2}$ year will be calculated. By taking Rupees $Rs21,780$ as principal, the S.I. for the next year will be calculated.
$S.I.=\frac{21,780\times \frac{1}{2}\times 10}{100}=Rs1,089$

Calculate the final amount and interest.
$\therefore$ Interest for the first 2 years $=(21,780-18,000)=Rs3,780$
And the interest for the next $\frac{1}{2}$ year = $1,089$
$\therefore \text{Total C.I.}=Rs(3,780+1,089)=4,869$
Now, amount, A = Principal + Compound interest
Amount $\left(A\right)$ = $(18,000+4,869)$
Amount $=Rs22,869$

(c)
Calculate the amount
Given,
Rate (R) = $8\%$ per annum or $4\%$ per half year
Time of years $=1\frac{1}{2}$ years
There will be \93\) half years in $1\frac{1}{2}$ years.
$\therefore \text{Amount (A)}=P{(1+\frac{R}{100})}^n$
$\Rightarrow A=[62,500{(1+\frac{4}{100})}^3]$

$\Rightarrow A=[62,500{\left(\frac{104}{100}\right)}^2]=[62,500{\left(\frac{26}{25}\right)}^2]$
$\Rightarrow A=70,304$

Calculate the interest
C.I. = Amount - Principle
$\Rightarrow C.I.=Rs70,304-Rs62,500$
$C.I.=Rs7,804$

(d)
Calculate the amount
Given,
Principal (P) $=Rs8,000$
Rate (R) $=9\%$ par annum or $\frac{9}{2}\%$ per half year
Time of years $=1$ year.
Three will be 2 half years in 1 year.
$\therefore \text{Amount (A)}=P{(1+\frac{R}{100})}^n$
$\Rightarrow A=[8,000{(1+\frac{9}{200})}^2]$
$\Rightarrow A=[8,000{\left(\frac{209}{100}\right)}^2]$
$\Rightarrow A=Rs8,736.20$

Calculate the interest
C.I. = Amount - Principal
$C.I.=A-P=Rs8,73620-Rs8,00$
$C.I.=Rs736.20$

Calculate the amount
Given,
Principal (P) $=Rs10,000$
Rate (R) = $8\%$ per annum or $4\%$ per half year
$\therefore \text{Amount (A)}=P{(1+\frac{R}{100})}^n$
$A=[10,000{(1+\frac{4}{100})}^2]$
$A=[10,000{(1+\frac{1}{25})}^2]=[10,000{\left(\frac{26}{25}\right)}^2]$
$\Rightarrow A=Rs10,816$

Calculate the interest

$C.I.=A-P=10,816-10,000$
$\Rightarrow C.I.=Rs816$