Question

$10000 is deposited in an account earning 4% interest compounded continuously. Use the continuous interest formula below to determine how long it takes for the amount in the account to double. Round answer to 2 decimal places. A = P e r t

_____years.

Answer 1

Answer:

The required number of years are 7.52 years.

Step-by-step explanation:

Given : $10000 is deposited in an account earning 4% interest compounded continuously.

To find : How long it takes for the amount in the account to double?

Solution :

Applying Continuous interest formula,

$A=Pe^{rt}$

Where, P is the principal P=$10000

r is the interest rate r=4%=0.04

t is the time

We have given, Amount in the account to double

i.e. A=2P

Substitute the value in the formula,

$2P=Pe^{rt}$

$2=e^{0.04t}$

Taking log both side,

$\log 2=\log (e^{0.04t})$

$\log 2=0.04t\times log e$

$t=\frac{\log 2}{0.04}$

$t=7.52$

Therefore, The required number of years are 7.52 years.