Question

A dinner set is sold for Rs. 1,500 cash or Rs.1000 cash down payment and Rs.545 to be paid in one installment after 6 months. Find the rate of interest charged under installment scheme.

Answer 1

Hint: This problem denotes the simple interest calculation. We have given the values of cash price and cash down payment with which we can calculate the principal amount. And with other values of time and interest given, we can be able to find the rate of interest charged by using simple interest, \[{\text{I}} = \dfrac{{{\text{P}} \times {\rm T} \times {\text{R}}}}{{100}}\]

Complete step-by-step answer:
Cash price of a dinner set= Rs. 1500.
Cash down payment of a dinner set = Rs. 1000.
Balance payment (P) = Cash price of dinner set – Cash down payment of a dinner set
That is,
Rs. $\left( {1500 - 1000} \right) = {\text{Rs}}{\text{. 500}}$
Therefore, Principal amount $ = {\text{Rs}}{\text{. 500}}$
One installment to be paid after six months = Rs. 545
Interest (I) to be charged = Amount paid in one installation after 6 months – Principal amount (initial value)
That is, from the above values
$ \Rightarrow {\text{Rs}}{\text{. }}\left( {545 - 500} \right) = {\text{Rs}}{\text{. 45}}$
Therefore, Interest amount$ = {\text{Rs}}{\text{. 45}}$
Time period (T) = 6 months = $\dfrac{6}{{12}}$years.
Let the rate of interest be R% per annum.
We know that, Simple Interest
$ \Rightarrow {\text{I}} = \dfrac{{{\text{P}} \times {\rm T} \times {\text{R}}}}{{100}}$
Where, I = Interest
P = Principal amount (initial value)
R = Rate of Interest per annum
T = Time (years)
$ \Rightarrow {\text{R = }}\dfrac{{100 \times {\text{I}}}}{{{\text{P}} \times {\text{T}}}}$
$ \Rightarrow {\text{R = }}\dfrac{{100 \times 45}}{{500 \times \dfrac{6}{{12}}}}$
$ \Rightarrow {\text{R = }}\dfrac{{100 \times 45 \times 12}}{{500 \times 6}} = 18$
$ \Rightarrow {\text{R = 18}}$
Hence, the rate of interest charged under the installment scheme is 18% per annum.

Note: Compound Interest is the addition of interest to the principal sum of interest on interest. We will be able to calculate compound interest using the formula${\text{A = P}}{\left( {1 + \dfrac{{\text{r}}}{{\text{n}}}} \right)^{{\text{nt}}}}$where ‘A’ is the final amount, ‘P’ is the initial principal balance, ‘r’ is the rate of interest, ‘n’ is the number of times interest applied per time period and ‘t’ is the number of time periods elapsed.