Question

at what time rs 10000 amounts to rs 14641 at the rate of 20% p.a. compounded half yearly
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Answer 1

Answer:

what time will 10000 Rs. amount to 13310 Rs. at 20% per annum compounded half yearly?

[A]3years

[B]2\frac{1}{2}years

[C]2years

[D]1\frac{1}{2}years

\mathbf{1\frac{1}{2}years}

The rate of interest is compounded half yearly,

∴ r = 10% per half year

Let time = \frac{T}{2}years = half years

According to the question,

Amount = P \left ( 1+\frac{R}{100} \right )^{t}

=> 13310 = 10000\left ( 1+\frac{10}{100} \right )^{T}

=> \frac{13310}{10000} = \left ( \frac{11}{10} \right )^{T}

=> \left ( \frac{11}{10} \right )^{T} = \frac{1331}{1000} = \left ( \frac{11}{10} \right )^{3}

=> T = 3 half years = 1\frac{1}{2} years

Hence option [D] is correct answer.

Answer 2

Answer:

2 years

Step-by-step explanation:

let n = no. of half years

14641=10000[1+10/100]^n

14641/10000= (11/10)^n

(11/10)^4 = (11/10)^n

SO n= 4 half years = 2years

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