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How long does it take for $50 to grow to $130 at 7% annual percentage rate compounded continuously?

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It will take about years for $50 to grow to $130 at 7% annual percentage rate when compounded continuously.
(Round to the nearest whole number as needed.)



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How long does it take for $50 to grow to $130 at 7% annual percentage rate compounded-example-1
User Shammir
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2 Answers

6 votes

Answer:

Explanation:

User Dennis Smit
by
9.1k points
4 votes

Answer:

Explanation:

The formula for continuously compounded interest is:

A = Pe^(rt)

where:

A = the final amount

P = the initial amount

r = the annual interest rate (as a decimal)

t = the time (in years)

We can use this formula to solve for t, the time it takes for $50 to grow to $130 at a 7% annual interest rate compounded continuously.

First, let's plug in the given values:

$130 = $50e^(0.07t)

Next, let's solve for t by isolating it on one side of the equation:

e^(0.07t) = $130/$50

e^(0.07t) = 2.6

Take the natural logarithm of both sides:

ln(e^(0.07t)) = ln(2.6)

0.07t = ln(2.6)

Solve for t:

t = ln(2.6)/0.07 ≈ 13.4 years

Therefore, it takes approximately 13.4 years for $50 to grow to $130 at a 7% annual interest rate compounded continuously.

User OwnageIsMagic
by
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