Question

The cost of a dining set is Rs. 24,000. Sindhu wants to buy it in 6 monthly installments. If she is offered 10% p.a. simple interest, find the EMI and the total amount paid by her.

Answer 1

We have $P=Rs.24,000$, $R=10\%$ and $T=6months=1/2year$. Here is no down payment. Hence the principal is P = Rs. 24,000. But we know that $E=nI-P$. Substitute this in the relation
$R=\frac{2400\times E}{n\left(\right(n+1)\times I-2E)}$.
We get
$R=\frac{2400(nI-P)}{n\left[\right(n+1)I-2(nI-P\left)\right]}=\frac{2400(nI-P)}{n[2-(n-1\left)I\right]}$
Hence
$nIR(2P-(n-1\left)I\right)=2400nI-2400P.$
This gives
$nIR\times (2400+(n-1\left)R\right)=P(2nR+2400)$.
We get a formula for I:
$I=\frac{P(2nR+2400)}{n(2400+(n-1\left)R\right)}$.
Here $P=24000$, $n=6$, $R=10$. Substituting these and simplifying the expression,
we obtain
$I=\frac{24000\left[\right(2\times 6\times 10)+2400]}{6[2400+(5\times 10\left)\right]}=\frac{201600}{49}\approx \mathrm{4114.30.}$
The monthly EMI is approximately Rs. 4,114.30. The total amount paid by her is
$4114.30\times 6\approx Rs.24,686$.