Question

find the amount which raman will get on Rs 81920, if he kept it for 9 months at 25/2% p.a. , interest being compounded quarterly​

Answer 1

Principal, P = Rs. 81920
Rate of interest, R = 25/2 %
Time, T = 9 months = 9/12 years = 3/4 years

We know that amount is equal to P[ 1 + (R/400)]^4T

Hence,

Amount = P [ 1 + ( R / 400 ) ] ^ 4T
=> Amount = 81920 [ 1 + { 25 / ( 2 * 400 ) } ] ^ [ 4 * ( 3 / 4 ) ]
=> Amount = 81920 [ 1 + ( 25 / 800 ) ] ³
=> Amount = 81920 [ 1 + ( 1 / 32 ) ]³
=> Amount = 81920 [ ( 32 + 1 ) / 32 ]³
=> Amount = 81920 [ 33 / 32 ]³
=> Amount = 81920 * ( 33 / 32 ) * ( 33 / 32 ) * ( 33 / 32 )
=> Amount = 2.5 * 33 * 33 * 33
=> Amount = 2.5 * 35937
=> Amount = Rs. 89842.50

Answer 2

$\bold{\huge{\underline{Question-}}}$

find the amount which raman will get on Rs 81920, if he kept it for 9 months at 25/2% p.a. , interest being compounded quarterly​ ?

$\bold{\huge{\underline{Answer-}}}$ According to the question we know that Rate of Interest is $\frac{25}{2} \%$,and principal is 81920 , or time is 9 month

We need to find Amount being compounded quarterly so, we changed the time in year ,

We know in a year 12 months

so, 9 month = $\frac{9}{12} = \frac{3}{4}$year

Now,

$\bold{Using \:the\: formula\: for\: Amount}$

so,

$A = p[1 + ( \frac{R}{400} )] {}^{4t}$

Now, Putting the above values

$A = 81920[1 + ( \frac{25}{2 \times 400} )]{}^{4 \times \frac{3}{4} }$

$A = 81920(1 + \frac{1}{32} ) {}^{ 3} \\ \\ \: \: \: \: = 81920( \frac{32 + 1}{32} ) {}^{3} \\ \\ \: \: \: \: = 81920( \frac{33}{32} ) {}^{3} \\ \\ \: \: \: \: = 2.5 \times 35937 \\ \\ \: \: \: = 89842.50$