Mathematics: How long will it take $40,000 to grow to $110,000 if it is compounded continuously at 6%

To make a the subject we proceed as follows:p=2a-3add 3 on both sides3+p=2a-3+3simplifying the above gives us:3+p=2adivide both through by 23/2+p/2=(2a)/2thusa=3/2+p/2...

How long will it take $40,000 to grow to $110,000 - id400001100001645382, krislinsanchez8088

Ответ:

rubianny03

15.03.2022

Mathematics

The formula for continuous compounding is given by

A = P. $e^{rt}$

where P is the initial or principal amount = $40,000

A is the amount at the end =$ 110,000

r is the rate of interest = 6% = 0.06

t is the time = the value we need to find

lets plug in the values

$110000= 40000 . e^{(0.06.t)}$

$\frac{110000}{40000} = e^{0.06t}$

$2.75= e^{0.06t}$

㏑(2.75) = ㏑[ $e^{0.06t}$ ]

㏑(2.75) = 0.06t

1.0116 = 0.06t

$t= \frac{1.0116}{0.06}$

t= 16.86 years

The time taken for $40000 to amount to $110000 is 16.86 years

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How long will it take $40,000 to grow to $110,000 if it is compounded continuously at 6%

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