A person invests 465 in an account that earns 25 annual inte

A person invests $465 in an account that earns 2.5% annual interest compounded continuously. Find when the value of the investment reaches $2,600. If necessary, round to the nearest hundredth. The investment will be reach $2,600 ______ in approximately years.

Solution

Continuous Compounding If P dollars is invested at an annual interest r compounded continuously, then the future value A after t- years is : A = Pe^(rt)

P = $ 465 ; A = $ 2600 ; r = 2.5%; t = ?

2600 = 465e^(0.025t)

5.59 =e^(0.025t)

Taking natural log on both sides:

ln( 5.59) = 0.025t

t = 68.84 yrs

The investment will be reach $2,600 in 68.84 in approximately years.