Question

What amount is to be repaid on a loan of Rs. 12000 for
1 year and 6 months at 10% per annum compounded half
Yearly..

Answer 1

Answer:

13891.5 rs , us to be paid

this is a compound interest problem we can solve this by the formula for coumpound interest which

p x (1+ r/100 ) ^n    ,where p= the initial amount , r = rate of interest , n time in yrs.

so, 12000(1 + 10/100) ^ ?    , but the time is 1 yr and 6 months but we have to write the time in yrs but we cant write 3/2 yrs because it is not a whole number

so in case of compounded half yearly we divide the rate of interest by 2 and multiply the time by 2

so the new expression is -

12000(1+5/100)^3

= 12000( 1 + 1/20 )^3

= 12000( 21/20) ^3

= 12000 ( 1.05 ) ^ 3

= 12000 x 1.157625

= 13891 .5 rs ( this is the amount to be paid)

but always remember to subtract the intial amount which here is 12k from thee final answer from the formula which here is 13891 .5 to get the compound interest.

Answer 2

Answer:

To find : Amount to be repaid on a loan

Given : P = 12000    R = 10 %          T = $1\frac{1}{2}$ yrs

As interest is compounded half yearly, so number of conversion periods in $1\frac{1}{2}$  years is 3,

therefore n=3

now , rate for half year = 1/2 x 10 % = 5%  

we know ,

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

$A = 12000(1 +\frac{5}{100} )^{3}$

   $= 12000(\frac{105}{100}) ^{3}$

On solving we get,

A = Rs 13891.50

as we know ,

compound interest = A - P

Therefore, C.I = 13891.50 - 12000

                       = 1891.50

Hence ,amount of  Rs 1891.50 is to be repaid.