Question

O
What time will 40,960 give an interest of a 8170 at 6 1/4%
p.a compounded anually
للص​

Answer 1

In a period of 3 years, Rs. 40,960 will give an interest of Rs.8170 at 6(1/4)% p.a. compounded annually.

Step-by-step explanation:

The sum of money, P = Rs. 40960

The compound interest, C.I. = Rs. 8170

The rate of interest, R = 6 $\frac{1}{4}$% p.a. = $\frac{25}{4}$% p.a.

The formula of compound interest is given by,

C.I. = P [(1 + $\frac{R}{100}$)ⁿ - 1]

Substituting the given values in the formula, we get

8170 = 40960 [(1 + $\frac{\frac{25}{4}}{100}$)ⁿ - 1]

⇒ 8170/40960 = [(1 + $\frac{1}{16}$)ⁿ - 1]

⇒ 0.199 + 1 = ($\frac{17}{16}$) ⁿ

⇒ 1.199 = ($\frac{17}{16}$) ⁿ

taking log on both sides

⇒ log 1.199 = n log 1.0625

⇒ 0.0788 = n × 0.0263

⇒ n = $\frac{0.0788}{0.0263}$

⇒ n = 2.99

⇒ n ≈ 3 years

Thus, the time period is 3 years.

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