## A person invests \$1,450 in an account that earns 6% annual interest compounded continuously. Find when the value of the investment reaches \$

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.

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3 days 2021-11-21T13:08:33+00:00 2 Answers 0

## Answers ( )

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)

Step-by-step explanation:

20.7 years

Step-by-step 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.