Question

Annabelle invested $5,900 in an account paying an interest rate of 2% 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 $7,440?

Answer 1

Answer:

Step-by-step explanation:

Continuous compounding has the form

$A=Pe^{rt}\\ \\ t=\frac{ln\frac{A}{P}}{r}\\ \\ t=\frac{ln\frac{7440}{5900}}{0.02}\\ \\ t\approx 11.6\\ \\ t=12$

Answer 2

Therefore it will take 12 years for the value of the account to reach $7,440.

What is Compound Interest ?

Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Annabelle invested amount $5900

Final Amount $7440

Rate = 2% compounded continuously

When compounded Continuously ,

$\rm A = P e^{rt}\\\\\\t=\dfrac{ln \frac{A}{P}}{r}\\\\\\\\t=\dfrac{ln \frac{7440}{5900}}{0.02}\\\\t= 12$

it will take 12 years for the value of the account to reach $7,440.

To know more about Compound Interest

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