Question

Ted invests $8,310 in a savings account with a fixed annual interest rate of 2% compounded continuously. How long will it take for the account balance to reach it take for the account balance to reach $9,751.88?

Answer 1

Answer: It will take 8 years.

Explanation:

Equation for interest compounded continuously:

`A=Pe^(rt)` , A = accumulated amount , P=Principal value , r =rate of interest , t= time.

Given: P= $8,310 , r = 2% , A= $9,751.88

`9751.88=8310e^(0.02t)\\\\\Rightarrow\ (9751.88)/(8310)=e^(0.02t)\\\\\Rightarrow\ 1.17351143201=e^(0.02t)`

Taking natural log on both sides

`\ln (1.17351143201)=\ln (e^(0.02t))\\\\\Rightarrow\ 0.160000478068=0.02t\\\\\Rightarrow\ t=(0.160000478068)/(0.02)\\\\\Rightarrow\ t=8.0000239034\approx8`

Hence, it will take 8 years.