Question

Drishti’s father wants to buy a house for Rs. 25,00,000. He wants to get a loan of Rs.15,00,000 from a bank and wishes to pay around Rs. 70,000 as a monthly installment to clear the loan. If the bank charges 9% interest, in how many months will Drishti’s father clear the loan amount?

Answer 1

Hint: First, let us write down all the given values and designate them a variable, next we will use the formula for monthly instalment (MI) = $\dfrac{\text{Simple Interest + Principal Amount}}{t\left( years \right)\times 12}$ and the formula for simple interest = $\dfrac{\text{P}\times \text{r}\times \text{t}}{100}$ along with basic mathematical operations to find the required result.

Complete step-by-step solution:
Here, we have the Principal amount (P) = Rs. 15,00,000; we also have the monthly instalment (MI) = Rs. 70,000 and the bank charges at 9%. which is the rate of interest (r) now here we have to find out how many months $\left( t \right)$ it took Drishti’s father to clear the loan.
Now, we know
Monthly Instalment (MI) = $\dfrac{\text{Simple Interest + Principal Amount}}{t\left( years \right)\times 12}$
Simple Interest = $\dfrac{\text{P}\times \text{r}\times \text{t}}{100}$
By using the above two formulas of Monthly instalment and simple interest let us find the total number of months Drishti’s father took to complete the loan.
$\Rightarrow70000 = \dfrac{\dfrac{15,00,000\times 9\times t}{100}+15,00,000}{t\times 12}$
$\Rightarrow70000\times t\times 12 = \dfrac{15,00,000\times 9\times t}{100}+15,00,000$
$\begin{align}
  &\Rightarrow 8,40,000t = 15,000\times 9\times t+15,00,000 \\
 &\Rightarrow 8,40,000t = 1,35,000t+15,00,000 \\
\end{align}$
Now, we will subtract by $1,35,000t$ on both the sides of the equation, we get
$\Rightarrow 8,40,000t - 1,35,000t = 1,35,000t-1,35,000t+15,00,000$
$\Rightarrow 705000t = 15,00,000$
Now, divide by 7,05,000 on both the sides of the equation, we get
$\begin{align}
 &\Rightarrow \dfrac{705000t}{705000} = \dfrac{15,00,000}{705000} \\
 &\Rightarrow t =2.1 \\
\end{align}$
Now, we know, 1 year = 12 months, therefore 2.1 years will be approximately equal to 25 months.
Hence, Drishti’s father will take 25 months to clear the loan amount.

Note: Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments. Simple interest is that type of interest which once credited does not earn interest on itself. To calculate the amount due at the end of the period, we can use the formula of amount = Principal + Simple Interest.