Question

A person invests $1,450 in an account that earns 6% annual interest compounded continuously. Find when the value of the investment reaches $2,500. If necessary round to the nearest tenth. The Investment will reach a value of $2.500 in approximately ____ years.

Answer 1

Years = natural log (total / principal) / rate

Years = natural log (2,500 / 1,450) / .06

Years = natural log (1.724137931) / .06

Years = 0.54472717542 / .06

Years = 9.078786257

Years = 9.1 (rounded)

Explanation:

Answer 2

20.7 years

Explanation:

Use the "compound amount, compounding continuously" formula:

A = Pe^(r · t)

Here,

A = $2,500 = $1,450e^(0.06 · t)

Divide both sides by $1,450: 1.724 = e^(0.06 · t)

Taking the natural log of both sides, we obtain:

ln 1.724 = (0.06 · t).

Finally, we divide both sides by 0.06, obtaining:

ln 1.724

------------ = t = 20.7

0.06

The Investment will reach a value of $2.500 in approximately 20.7 years.