Question

difference between the interest for first and second year on the sum of money compounded annually is 30 rupees . If the rate is 5%,what was the sum of money deposited?​

Answer 1

Given:

The difference between the interest for the first and second year on the sum of money compounded annually is 30 rupees.

To Find:

If the rate is 5%, what was the sum of money deposited?​

Solution:

Before solving the sum we should know the formula for the amount for compound interest which is,

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

where,

          A= amount at the end of the time period

          P= principal amount

          r= rate of interest

          n= time period

now Rs30 is equal to the difference of the interest for the first and second year, so

The interest for the 1st year is,

$I_{1}=P(1+0.05)-P\\=0.05P$

And the interest for the 2nd year will be,

$I_{2}=P(1+0.05)^2-P(1+0.05)\\=1.1025P-1.05P\\=0.0525P$

Now the difference between the two will be,

$30=I_{2}-I_{1}\\30=0.0525P-0.05P\\P=\frac{30}{0.0025}\\=12000$

Hence, the sum of the money deposited is Rs12000.