Question

rupees 18000 for 2 whole no. 1 upon 2 years at 10% per annum compounded annually

Answer 1

Given Principal= P= 18000

Rate of interest Per Annum= i = 10%

Time = n = 2 1/2 = 2.5 years

Lets do it two parts 2 years and half year

Compounded Amount = P(1+i)^n = 18000(1+10/100)^2

= 18000(1 + 0.1)^2

=18000(1.1)^2

=18000(1.21)

= 21780..

For remaining half year ..Rate of interest will be = 10%/2 =5% ..period will be 1

= 21780(1+5/100)^1

= 21780(1 + 0.05)

=21780(1.05)

=22869

Answer 2

GIVEN :-

• principal ( p ) = rs 18000

• time ( n ) or ( t ) = 2 ½ years

• rate ( r ) = 10%

TO FIND :-

• amount ( a )

SOLUTION :-

[ SINCE TIME IS 2½ YRS SO WE WILL TAKE 2 YRS AS COMPOUND AND ½ YRS AS SIMPLE INTEREST ]

and total amount will be

A = INTEREST ( OF 2½ YRS ) + PRINCIPAL

compound Interest ( 2yrs )

time = 2 yrs

rate = 10%

principal = 18000

no we know the formula for compound interest :-

$\implies \boxed{\rm{a = p(1 + \dfrac{r}{100}) {}^{n} }}$

where ,

a = amount

n = time in yrs

r = rate

p = principal

$\implies \rm{a =18000 (1+ \dfrac{10}{100}) {}^{2} }$

$\implies \rm{a =18000 ( \dfrac{10 + 100}{100}) {}^{2} }$

$\implies \rm{a =18000 ( \dfrac{110}{100}) {}^{2} }$

$\implies \rm{a =18000 ( \dfrac{11}{10}) {}^{2} }$

$\implies \rm{a =18000 ( \dfrac{11}{10}) ( \dfrac{11}{10} ) }$

$\implies \rm{a =180 \times 11 \times 11}$

$\implies \rm{a =180 \times 121 }$

$\implies \rm{ \bf \: a =21780 \: rs}$

NOW ,

AMOUNT = PRINCIPAL + INTEREST

21780 = 18000 + INTEREST

INTEREST = 21780 - 18000

INTEREST = 3780 rs

now for

simple interest of ½ yrs

time = ½ yrs

rate = 10%

new principal = 21780 rs

no we know the formula simple interest :-

$\implies \boxed{\rm{si= \dfrac{p \times r \times t}{100} }}$

$\implies \rm{si= \dfrac{21780 \times 10 \times 1}{100 \times 2} }$

$\implies \rm{si= \dfrac{2178 }{ 2} }$

$\implies \rm{ \bf \: si= 1089 \: rs }$

now ,

total amount = ( interest for 2½ yrs ) + principal

total amount = ( 3780 + 1089 ) + 18000

total amount = 4869 + 18000

$\implies \boxed{ \boxed{ \rm{ total \:interest \: = 4869\: rs }}}$

$\implies \boxed{ \boxed{ \rm{ total \: amount \: = 22869 \: rs }}}$