Question

in how many years will ruppes 7,000 amount to rupees 9,317 at 10 % per annum compund instrest

Answer 1

CORRECT QUESTION :

• ➬ In how many years will Rs. 7,000 amount to Rs. 9,317 at 10 % per annum compound interest.

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SOLUTION :

❒ Given :-

• Principle, P = Rs. 7000

• Amount, A = 9317

• Rate of Interest, r = 10% p.a.

• Type of Interest = Compound interest

❒ To Find :-

• No. of years, n = ?

❒ Required Formula :-

• In case of interest compounded annually,

$\: \: \: \: \: \: \: \: \: \: \bigstar \: \: \boxed{ \large{ \bold{ \: A = P \: (1 + \frac{r}{100}) {}^{n} \: }}}$

❒ Calculation :-

• Using the formula,

$\bigstar \: \: \sf{A = P \: (1 + \frac{r}{100}) {}^{n}} \\ \\ \sf{ \implies \: 9317 = 7000 \: (1 + \frac{10}{100} ) {}^{n}} \: \: \\ \\ \sf{\implies \: 9317 = 7000 \: ( \frac{100 + 10}{100}) {}^{n}} \\ \\ \sf{\implies \: 9317 = 7000 \: ( \frac{110}{100} ) {}^{n}} \: \: \: \: \: \: \: \: \\ \\ \sf{\implies \: 9317 = 7000 \times ( \frac{11}{10} ) {}^{n}} \: \: \: \: \: \: \: \\ \\ \sf{\implies \: \frac{9317}{7000} = (\frac{11}{10} ) {}^{n}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{\implies \: \frac{1331}{1000} =(\frac{11}{10}) {}^{n}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{\implies \: \frac{(11) {}^{3} }{(10) {}^{3} }= ( \frac{11}{10}) {}^{n}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{\implies \: ( \frac{11}{10} ) {}^{3} = ( \frac{11}{10} ) {}^{n}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{\implies \: 3 = n} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large{ \sf{\therefore \: \underline{ \: n = 3 \: }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• ➬ Hence, the number of year, n = 3 years.

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ANSWER :

• In 3 years will Rs. 7,000 amount to Rs. 9,317 at 10 % per annum compound interest.

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KNOW MORE :

✪ Interest :-

• When a person borrows a sum of money from another person or bank or any other financial institutions for a period, on the expiry of that period, the person (borrower) has to repay his debg by paying some extra money along with the original sum of money. The extra sum of money is known as Interest.

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

✪ Types of Interest :-

• [1] Simple Interest

• [2] Compound Interest

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

✪ Simple Interest :-

• When the interest is calculated on the initial sum of money borrowed throughout the specified period, then the interest obtained is known as Simple Interest.

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

✪ Compound Interest :-

• When the interest that falls due at the end of a specified time period is added to the principal and the amount so obtained becomes the principal for calculating interest for the subsequent period and the process goes on, thus the interests obtained is knowns as Compound Interest.