Question

21
Find the effective rate of interest if an amount of 30,000 deposited in a bank. For 1 year
at the rate of 10% p.a. compounded semi annually.
(a) 10.05%
(b)
10.10%
(c) 10.20%
(d)
10.25%​

Answer 1

The value of  the effective rate of interest is 10.25% and option(d) is correct.

Step-by-step explanation:

Given:

An amount of 30,000 deposited in a bank.

For 1 year at the rate of 10% p.a. compounded semi annually.

To Find:

The value of  the effective rate of interest.

Formula Used:

$CI=Y(1+\frac{Z}{N\times100} )^{NT} -Y$   ------------- formula no.01.

CI=Compound Interest

X= represents the new principal sum or the total amount of money after compounding period

Y= represents the original amount or initial amount

Z= is the annual interest rate(in percentage)

T= represents the number of years

N= the number of times interest is compounded in a  year

Solution:

As given-an amount of 30,000 deposited in a bank.

               -for 1 year at the rate of 10% p.a. compounded semi annually.

Y=30000   ,  Z=10% per annum    ,T = 1 Year   and N=2  for compounded semi annually.  

Applying formula no.01. Putting  values of Y,Z,T and N in formula

$CI=Y(1+\frac{Z}{N\times100} )^{NT} -Y$

     $=30000(1+\frac{10}{2\times100} )^{2\times1} -30000$

      $=30000(1+\frac{1}{20} )^{2} -30000$

     $=30000(\frac{21}{20})^{2} -30000$

     $=30000(1.05)^{2} -30000$

     $=30000\times1.1025 -30000$

     $=33075-30000$

     $=3075$

Compound Interest =3075

An amount deposit  in bank =30000

Hence, the effective  rate of interest %  $=\frac{3075\times100}{30000}$

                                                                 $=10.25\%$

Thus,the value of  the effective rate of interest is 10.25% and option(d) is correct.

PROJECT CODE #SPJ1

Answer 2

The effective interest rate 10.25 %

Given : Amount deposited in the bank is 30,000 Rs

Time is 1 year

Interest rate compounded semiannually is 10 % per annum

To Find : The effective interest rate

Solution :  The effective interest rate 10.25 %

It is given that an amount of 30,000 deposited in a bank. For 1 year

at the rate of 10% p.a. compounded semi annually.

We have to find the effective interest rate

Now the formula of effective interest rate is

$r = (1+\frac{i}{n}) ^{n}-1$

where r is effective interest rate

n is the compounding frequency

i is interest rate given

so it is given that

i is 10 %

n is 2

r = ?

so r = $(1+\frac{0.10}{2}) ^{2}-1$

r = $(1+0.05)^{2}-1$

r = $1.05^{2}-1$

r = 1.1025 -1

r = 0.125

r = 10.25 %

So effective interest rate is 10.25 %

#SPJ1