Question

Deshawn invests $5,000 in a savings account that earns 6% annual interest, compounded continuously. How long will it take to double his money?

Answer 1

Answer:

Step-by-step explanation:

Investment = $5,000

Annual Interest = 5%

5000/100 x 5/1

50×5 = 250

First year interest = $250

Therefore, 250 x 20

= $5,000

It will take him 40 years.

Answer 2

It will take about 11.55 years to double his money.

Important information:

• Principal value = $5,000
• Rate of interest = 6% compounded continuously.

Continuous compound interest:

The formula for the amount in continuous compound interest is:

$A=Pe^{rt}$

Where A is the amount, P is the principal, r is the rate of interest and t is time in years.

Substitute $A=10000, P=5000,r=0.06$.

$10000=5000e^{0.06t}$

$\dfrac{10000}{5000}=e^{0.06t}$

$2=e^{0.06t}$

Taking ln on both sides, we get

$\ln 2=\ln e^{0.06t}$

$\ln 2=0.06t$

$\dfrac{\ln 2}{0.06}=t$

$t=11.55245$

$t\approx 11.55$

Therefore, it will take about 11.55 years to double his money.

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