If an investment of Rs. 12000 becomes Rs. 72000 in 4 years, then the compound annual growth rate is: Option 1: (^4√6-1)/100 % Option 2: (^4√6+1)/100 % Option 3: (^4√6+1) x 100 % Option 4: (^4√6-1) x 100 %

Answer: (^4√6-1) x 100 %. Solution: The compound interest formula is: A = P(1 + r/100)^n where P = 12000, A = 72000, and n = 4. 72000 = 12000(1 + r/100)^4 72000/12000 = (1 + r/100)^4 6 = (1 + r/100)^4 4√6 = 1 + r/100 r/100 = 4√6 - 1 r = (4√6 - 1) x 100% Therefore, the compound annual growth rate is (4√6 - 1) x 100%.

Statistics & Applications

Financial Math

Medium

applied

If an investment of Rs. 12000 becomes Rs. 72000 in 4 years, then the compound annual growth rate is:

$\frac{^4\sqrt{6}-1}{100}$ %

$\frac{^4\sqrt{6}+1}{100}$ %

$(^4\sqrt{6}+1) \times 100$ %

$(^4\sqrt{6}-1) \times 100$ %

✅ Correct Option: 4

The compound interest formula is:

$A = P\left(1 + \dfrac{r}{100}\right)^n$

where $P = 12000$ , $A = 72000$ , and $n = 4$ .

$72000 = 12000\left(1 + \dfrac{r}{100}\right)^4$

$\dfrac{72000}{12000} = \left(1 + \dfrac{r}{100}\right)^4$

$6 = \left(1 + \dfrac{r}{100}\right)^4$

$\sqrt[4]{6} = 1 + \dfrac{r}{100}$

$\dfrac{r}{100} = \sqrt[4]{6} - 1$

$r = \left(\sqrt[4]{6} - 1\right) \times 100\%$

Therefore, the compound annual growth rate is $\left(\sqrt[4]{6} - 1\right) \times 100\%$ .

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Solution

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