Question

Shrinivas deposited $1300 in an account which pays 8% annual interest, compounded continuously. How long will it take to reach $3500?
Select one:
O a. 12.4 years
O b. 9.2 years
O c. 176 years
O d. 1.2 years

Answer 1

Answer: a. 12.4 years

Step-by-step explanation:

Function to represent exponential growth continuously:

$A=A_0e^{rt}$  ...(i)

, where $A_0$ = initial amount, r= rate of interest ( in decimal) , A = Amount after t years.

As per given , we have

$A_0=\ 1300\\\\r=8\%=0.08\\\\ A=\ 3500$

To find : t

Put all values in (i) ,

$3500=(1300)e^{0.08t}\\\\\Rightarrow\ 2.6923077=e^{0.08t}$

Taking natural log on both sides

$\ln(2.6923076)= 0.08t\\\\\Rightarrow\ 0.99039867=0.08t\\\\\Rightarrow\ t=\dfrac{0.99039866}{0.08}=12.37998325\approx12.4$

Hence, it would take 12.4 years.

so, the correct option is a. 12.4 years .