Question

$800 is invested in C.I where the rate of interest is 20% per year. If interest is compounded half yearly, what will be the accumulated value and C.I after 2 years ?​

Answer 1

The formula to find accumulated value in C.I is 

A  =  P(1 + r/n)nt

Where,

•A -----> Accumulated value (final value )  

•P -----> Principal (initial value of an investment) 

•r -----> Annual interest rate (in decimal)

•n -----> Number of times interest compounded per year

•t -----> Time (in years)

•C.I -----> Amount of interest

Here,

P  =  800

r  =   20%   =  0.2

n  =  2

t  =  2

Then, the accumulated value is

A  =  800(1 + 0.1)⁴

A  =  800(1.1)⁴

A  =  800 ⋅ 1.4641

A  =  $1171.28

Compound interest is

C.I  =  A - P 

C.I  =  1171.28 - 800

C.I  =  $371.28

Therefore accumulated value and CI after 2 years $1171.28 and $371.28 respectively.

Answer 2

Since it is half yearly
So t=2*2=4
Rate=20/2=10
So amount = 800(1+0.1)^4
=800(1.1)^4
=1171.28
CI= 1171.28-800=$371.28