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Five thousand dollars compounded annually at an $x\%$ interest rate takes six years to double. At the same interest rate, how many years will it take $\$300$ to grow to $\$9600$? Your Answer

Respuesta :

letmeanswer

30 years

Explanation:

In order to find out the number of years, the following calculation is needed to be made.

As per the given data, it has been given that $5000 doubles in 6 years

[tex]10,000=5000(1+x / 100)^{\wedge} 6[/tex]

Now, dividing both sides by 5000

[tex]2=(1+x / 100)^{\wedge 6}[/tex]

on solving the above equation, we get

x = 12.246

at the same interest rate

[tex]9600=300(1+.12246)^{\wedge} \mathrm{t}[/tex]

t = 30

so, in 30 years $ 300 will grow to $ 9600

Thus, the correct answer is 30 years.

Tundexi

At same interest rate, it take 30 years to grow $300 to $9600.

Since it is given that $5,000 doubles in 6 years

10,000 = 5000 (1 + x/100)^6

Divide both sides by 5000

2 = (1 + x/100)^6

x = 12.246

At same interest rate, will be input for (x)

9600 = 300 (1 + 0.12246)^t

Divide both sides by 300

32 = (1 + 0.12246)^t

t = 30

In conclusion, at same interest rate, it take 30 years to grow $300 to $9600.

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