In how many years, will a sum of money double itself at 10% C.I.: 1. 5 years 2. 10 years 3. 8 years 4. none of these

Given, rate of interest = 10% Let sum of money be ₹ P and time be n years. Using the formula, A = P ₹ P doubles itself in n years. A = 2P Substituting values in formula, we get : Substituting, n = 5 in R.H.S. of equation (1), (1.1)5 = 1.61 Thus, n 5. Substituting, n = 10 in R.H.S. of equation (1), (1.1)10 = 2.59 Thus, n 10. Substituting, n = 8 in R.H.S. of equation (1), (1.1)8 = 2.14 Thus, n 8. Hence, option 4 is correct option.

Mathematics

In how many years, will a sum of money double itself at 10% C.I.:
5 years
10 years
8 years
none of these

Compound Interest

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Answer

Given, rate of interest = 10%

Let sum of money be ₹ P and time be n years.

Using the formula, A = P $\Big(1 + \dfrac{R}{100}\Big)^n$

₹ P doubles itself in n years.

A = 2P

Substituting values in formula, we get :

$\Rightarrow 2P = P\Big(1 + \dfrac{10}{100}\Big)^n \\[1em] \Rightarrow 2 = (1 + 0.1)^n \\[1em] \Rightarrow 2 = (1.1)^n \text{ …………(1)}$

Substituting, n = 5 in R.H.S. of equation (1),

(1.1)⁵ = 1.61

Thus, n ≠ 5.

Substituting, n = 10 in R.H.S. of equation (1),

(1.1)¹⁰ = 2.59

Thus, n ≠ 10.

Substituting, n = 8 in R.H.S. of equation (1),

(1.1)⁸ = 2.14

Thus, n ≠ 8.

Hence, option 4 is correct option.

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Mathematics

In how many years, will a sum of money double itself at 10% C.I.:
5 years
10 years
8 years
none of these

Compound Interest

Answer

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In how many years, will a sum of money double itself at 10% C.I.:5 years10 years8 yearsnone of these

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