Question

A person borrows a sum Rs 2048 at 6 1/4 % per annum, compounded annually. On the same dayon at the same rate of interest, but compounded semi annuallyhe lent out his money to another person at the same rate of interestannually. Find his gain after1 1/2years.​

Answer 1

Therefore he gain after $1\frac12$ years is Rs 2.0625.

Explanation:

Compound interest formula:

$A=P(1+r)^t$

A= Amount after n years

P=Initial amount

r= Rate of interest

t= time.

Given that, a person borrow a sum Rs 2048 at $6\frac{1}{4}$ % per annum, compounded annually for $1\frac12$ years.

Here P= Rs 2048 , r= $6\frac{1}{4}$ % =0.0625

Since $1\frac12$  is not an integer. So, first we have find out the interest for 1 year. Then we need to  find out the interest for $\frac12$.

Simple interest for the first year interest = Compound  interest for the first year interest.

The interest for 1 year is $=Prt$

                                        =2048×0.0625×1

                                       =Rs 128.

Now Principal for $\frac12$ year is = Rs(2048+128)

                                            =Rs 2176

The interest for $\frac12$ year is $=Prt$

                                       $=2176 \times 0.625\times \frac12$

                                      =Rs 68.

Therefore total amount that he will pay after  $1\frac12$ years is = Rs (2176+68) = Rs 2244.

Again given that on the same day he lent out his money to another person same rate of interest but compounded semiannually.

Formula for semi annually compound interest:

$A=P(1+\frac rn)^{nt}$

A= Amount after n years

P=Initial amount

r= Rate of interest

t= time.

Here P= Rs 2048 , r= $6\frac{1}{4}$ % =0.0625, $t=1\frac12=\frac32$ years, n=2[ semi annually]

$A= 2048(1+\frac {0.0625}{2})^{\frac32 \times 2}$

   $=2048(1.03125)^3$

   =Rs 2246.0625

Therefore he gain after $1\frac12$ years is Rs(2246.0625-2244)=Rs 2.0625