Naomi invested $920 in an account paying an interest rate of 4.7% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $2,310?

 

Answer is:

The value of the account to reach $2,310, in 9 years.

Step-by-step explanation

Naomi invested $920 in an account paying an interest rate of 4.7% compounded continuously.

Hence, Value of amount in t years = ?920e4.7%t=920e1004.7t?=920e0.047t?

Value of amount is $2320 in t year.

??2320=920e0.047t?

??e0.047t=92232??

Taking log on both sides, we get

?0.047t=log(232)−log(92)?

??t=471000?(log(232)−log(92))?

??t=471000?(0.4017)≈8.5468?

So, It take 9 year, for the value of the account to reach $2,310.