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statuscvo [17]
3 years ago
15

Ted invests $8,310 in a savings account with a fixed annual interest rate of 2% compounded continuously. How long will it take f

or the account balance to reach it take for the account balance to reach $9,751.88?
Mathematics
1 answer:
Vsevolod [243]3 years ago
8 0

Answer: It will take 8 years.

Step-by-step 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\ \dfrac{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=\dfrac{0.160000478068}{0.02}\\\\\Rightarrow\ t=8.0000239034\approx8

Hence, it will take 8 years.

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