Question

1 Mr. Johnson borrowed Rs 8000
for 4 years to make home improvements.
If he repaid to total of Rs 10,3201
at what interest rate. did he borrow
the money?​

Answer 1

➤ Given :-

Principle :- ₹8000

Time :- 4 years

Total Amount :- ₹103201

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➤ To Find :-

The rate of interest applied to the loan.

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★ How to do :-

Here, we are given with the principle amount, the time taken to give back money and also the total amount returned back at end of the time period. We are asked to find the rate of interest that had been applied to this loan. So, first we should find the interest amount or simple interest of this sum by subtracting the total amount and the principle. The particular formula is given while solving. Later, we can find the rate of interest being applied to Mr.Johnson. The appropriate formula for the same is given while solving the problem. So, let's solve!!

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➤ Solution :-

First, we should find the simple interest.

Simple Interest :-

${\tt \leadsto \underline{\boxed{\tt Total \: Amount - Principle}}}$

Substitute the given values.

${\tt \leadsto 103201 - 8000}$

Subtract to get the value of simple interest.

${\tt \leadsto Rs \: \: 95201}$

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Now, find the rate of interest by using the formula given below.

Rate of interest :-

${\tt \leadsto \underline{\boxed{\tt \dfrac{SI \times 100}{P \times T}}}}$

Substitute the given values.

${\tt \leadsto \dfrac{95201 \times 100}{8000 \times 4}}$

Cancel the zeros in numerator and denominator.

${\tt \leadsto \dfrac{95201 \times 1 \cancel{00}}{80 \cancel{00} \times 4} = \dfrac{95201 \times 1}{80 \times 4}}$

Now, just multiply the values in denominator and write it in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{95201}{320} = 297.5 \bf\% \tt \: \approx}$

$\Huge\therefore$ The rate of interest applied to the given sum is 297.5%.

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$\dashrightarrow$ Some related formulas :-

$\small\boxed{\begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Simple \: Interest :- \dfrac{P \times R \times T}{100}} \\ \\ \bigstar \: \sf{Principle :- \dfrac{SI \times 100}{R \times T}} \\ \\ \bigstar \: \sf{Time :- \dfrac{SI \times 100}{P \times R}}\end{array}}$