How long will it take $200 to double if it is invested at 10% interest compound quarterly

Round answer to the nearest 100th.

400 = 200(1 + .10/4)^(4t)

2 = 1.025^(4t)

log(2) = (4t)log(1.025)

t = log(2) / (4log(1.025)) = 7.02 years

is 400

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I wish to answer in a different way.
Use the empirical rule that any amount becomes doubled in 72/r years where r is the rate of interest in percentages.
If the rate of interest is 10%, then 72/10 = 7.2 years needed to get the amount doubled.
If the rate of interest is 8%, then 72/8 = 9 years needed to get the amount doubled.
If the rate of interest is 6%, then 72/6 = 12 years needed to get the amount doubled.
The result is an approximation but it gives a rough idea about the time required for getting the amount doubled BUT it is not to be used in academic matters.
Follow the procedure given by the first answerer.

Just substitute 115 in place of 72 to get the amount trebled.

How long will it take $200 to double
if it is invested at 10% interest compound quarterly?
Round answer to the nearest 100th.

$200(1.025)^Q = $400
(1.025)^Q = 2
Q = 28.071
It will take 7.02 years.

i=0.10/4
i=0.025
200(1+i)^t=400
(1+.025)^t=2
tlog(1.025)=log(2)
t=log(2)/log(1.025)
t=28.071 quarters
t= 7 years

Using the formula: A=P(1+R/N)^NT, you can plug and solve.

400 = 200 * (1 + 0.1/4)^(4 * x)
2 = (1.025)^(4x)
ln(2) = 4x * ln(1.025)
x = ln(2) / (4 * ln(1.025))
x = 7.0177586314846574484950049526313

7.02 years