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

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=(0.99039866)/(0.08)=12.37998325\approx12.4`

Hence, it would take 12.4 years.

so, the correct option is a. 12.4 years .