Question

The Johnson family want to start a college fund for their daughter Gabriella. They put $63, 000 in to an account that grows at a rate of 2.55% per year, compounded quaterly. Given the function G(t)= 63,000(1+ .0255/4)^ 4t, where G(t) represents the amount of money in the account t years after the account is opened, given that no more money is deposited into or withdrawn from the account.

Calculate the number of years it will take for the account to reach approximately $150,000, to the nearest hundredth of a year.

Answer 1

• 34.13 years

Explanation:

Given formula:

• G(t)= 63000(1 + 0.0255/4)^4t

Need to find the value of t when G(t) = 150000

• 150000 = 63000( 1+ 0.0255/4)^4t
• ( 1+ 0.0255/4)^4t = 150000/63000
• ( 1+ 0.0255/4)^4t = 2.3809
• 4t* log( 1+ 0.0255/4) = log 2.3809
• 4t *0.00275983965 = 0.37674115501
• t = 0.37674115501/(4*0.00275983965)
• t = 34.13 years rounded