Question

the time taken for rupees 4400 to bkn Rupees 4851 at 10 % compounded half yearly is solve this problem​

Answer 1

The time taken for rupees 4400 to becomes Rupees 4851 at 10 % compounded half-yearly is 1 year.

Step-by-step explanation:

Principal, P = Rs. 4400

Amount, A = 4851

Since the interest is compounded half-yearly, so the rate of interest,

[R/2]% = [10/2]% = 5%

The formula for finding the amount in case of interest compounded half-yearly is given by,

A = P [1 + $\frac{\frac{R}{2}}{100}$]²ⁿ

Here,

n = Time (in years)

2 = No. of times compounded per year [i.e., there are 2 half-years in a year]

Now, by substituting the given values in the formula, we get

4851 = 4400 [1 + (5)/100]²ⁿ

⇒ 4851/4400 = [1 + 1/20]²ⁿ

⇒ 1.1025 = [21/20]²ⁿ

⇒ 1.1025 = [1.05]²ⁿ

Taking log on both sides

⇒ log 1.1025 = log [1.05]²ⁿ

⇒ log 1.1025 = 2n * log [1.05] ……. [since log aᵇ = b log a]

⇒ 0.0423 = 2n * 0.0211

⇒ 0.0423 = 0.0422 * n

⇒ n = 0.0423/0.0422

⇒ n = 1 year

Answer 2

Step-by-step explanation:

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