Adrian invested $790 in an account paying an interest rate of 6.9% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $2,550?

If the invested amount is 'P', the rate of interest is r%, and the time of investment is 'n' years, then the compound interest after mentioned duration is = P[1 - [tex]e^{rn}[/tex]]

Given, the invested amount (P) = $790.

Rate of interest (r) = 6.9% = 0.069.

Let, the amount is invested for 'n' years.

The value of the amount after 'n' years = $2550.

Now, as per compound interest:

A = P. [tex]e^{rn}[/tex]

⇒ 2550 = 790 [tex]e^{(0.069n)}[/tex]

⇒ [tex]e^{(0.069n)}[/tex] = (2550 ÷ 790)

⇒ [tex]e^{(0.069n)}[/tex] = 3.23

⇒ 0.069n = 1.172

⇒ n = 17

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Adrian invested $790 in an account paying an interest rate of 6.9% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $2,550?​

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What is the compound interest?

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Adrian invested $790 in an account paying an interest rate of 6.9% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $2,550?