Question

Calculate the compound interest on Rs. 15,000 in 3 years; if the rates of interest for successive years be \[6\% \], \[8\% \] and \[10\% \] respectively.
A.\[{\rm{Rs}}.3,879.20\]
B.\[{\rm{Rs}}.3,889.20\]
C.\[{\rm{Rs}}.3,789.20\]
D.\[{\rm{Rs}}.3,689.20\]

Answer 1

Hint: Here we will firstly find the interest of the first year on the principle using the formula of the interest on some principal amount. Then we will add the interest in the principal amount to get the new principal amount and then we will apply the interest formula to get the interest of the second year. Similarly, we will find the interest for the third year. Then we will add the interest of the first year, second year, and third year to get the total interest.

Formula used:
Interest \[ = \dfrac{{PRN}}{{100}}\] where, \[P\] is the principal amount, \[R\] is the rate of interest and \[N\] is the time period.

Complete step-by-step answer:
Given principal amount is Rs. 15,000 i.e. \[P = Rs.15000\].
Now we will find the interest for the first year. It is given that the rate of interest for the first year us equal to \[6\% \] i.e. \[R = 6\% \]. Therefore
Interest of first year \[ = \dfrac{{15000 \times 6 \times 1}}{{100}} = Rs.900\]
Now we will calculate the interest of the second year.
But the principal amount changes for the second year. We will add the interest of the first-year to the principal to get the principal from the second year. Therefore, we get
Principal amount becomes \[P = 15000 + 900 = {\rm{Rs}}.15900\]
It is given that the rate of interest for the second year is 8% i.e. \[R = 8\% \]. Therefore, we get
Interest of second year \[ = \dfrac{{15900 \times 8 \times 1}}{{100}} = {\rm{Rs}}.1272\]
Now we will find the interest of the third year.
Again, the principal amount changes for the third year. We will add the interest of the second year to the principal of the second year to get the principal from the third year. Therefore, we get

Principal amount becomes \[P = 15900 + 1272 = {\rm{Rs}}.17172\]
It is given that the rate of interest for the third year is 10% i.e. \[R = 10\% \]. Therefore, we get
Interest of third year \[ = \dfrac{{17172 \times 10 \times 1}}{{100}} = {\rm{Rs}}.1717.20\]
Now we will add the interest of the first year, second year and third year to get the interest for the 3 year. Therefore, we get
Total interest \[ = 900 + 1272 + 1717.20 = {\rm{Rs}}.3,889.20\]
Hence, the compound interest on Rs. 15,000 in 3 years; if the rates of interest for successive years be \[6\% \], \[8\% \] and \[10\% \] respectively is \[{\rm{Rs}}.3,889.20\].
So, option B is the correct option.

Note:Here we should note that while calculating the interest we should take the rate of interest in percentage in the formula of the interest. In simple interest, the interest per year remains constant over the period of time but in case of the compound interest, interest per year varies and it goes on increasing over the period of time. Interest is generally used in financial services. Interest can be yearly, monthly, quarterly, or semiannually.