Question

A principal amount of $600 is placed into a bank account compounded continuously at 3.5%. How long does it take for the amount to reach $1000?

Answer 1

For investments compounded continuously, we have


`A = Pe^(rt)`

where P is the principal amount and A is the new amount after a period of time t.

Given the information that we have, we can solve for the time taken for the principal amount to reach $1000 as shown below.


`1000 = 600(e^(0.035(t)))`

`(1000)/(600) = e^(0.035t)`

For powers of e, we can use the natural logarithmic function, ln(). Recall that


`x = ln(e^(x))`

Using what we know, we can solve for t in our equation.


`ln((1000)/(600)) = ln(e^(0.035t))`

`ln((5)/(3)) =0.035t`

`t = (ln((5)/(3)))/(0.035)`

`t = 14.59`

From this, we can see that it will take about 15 years for a principal amount of $600 to reach $1000 when compounded continuously at 3.5%.

Answer: 15 years