Question

Suzie invests $500 in an account that is compounded continuously at an annual interest rate of 5%, according to the formula A=Pe^rt, where A is the amount accrued, P is the principle, r is the rate of interest, and t is the time, in years. Approximately how many years will it take for Suzie's money to double?

a. 1.4
b. 6.0
c. 13.9
d. 14.7

Answer 1

Answer:

c. 13.9

Step-by-step explanation:

We have been given that Suzie invests $500 in an account that is compounded continuously at an annual interest rate of 5%. We are asked to find the time it will take for Suzie's money to double.

We will use continuous compounding interest formula to solve our given problem.

$A=P\cdot e^{rt}$, where A is the amount accrued, P is the principle, r is the rate of interest, and t is the time, in years.

$5\%=\frac{5}{100}=0.05$

Double of $500 would be $1000.

$1000=500\cdot e^{0.05t}$

$\frac{1000}{500}=\frac{500\cdot e^{0.05t}}{500}$

$2=e^{0.05t}$

Take natural log of both sides:

$\text{ln}(2)=\text{ln}(e^{0.05t})$

$\text{ln}(2)=0.05t\cdot \text{ln}(e)$

$0.6931471805599453=0.05t\cdot 1$

$\frac{0.6931471805599453}{0.05}=\frac{0.05t}{0.05}$

$13.8629436=t$

$t\approx 13.9$

Therefore, it will take 13.9 years for Suzie's money to double and option 'c' is the correct choice.