Question

Roberta deposited 3,116.92 into savings account with an inteest rate of 3.9% compounded quarterly. About how long will it take for the account to be worth 7,000?

Answer 1

the answer is approximated 83 quarters or 21 years

Step-by-step explanation:

they key in this question is to take into account the word "compounded quarterly" it means that every quarter there is paid
`(0.039)/(4)=0.975\%`. So the process to obtain the answe is as follows:

`3116.92*(1+0.975\%)^(n)=7000`

note here that n is the number of quarters needed for accumulating 7.000 using an interest rate of 0.975%, so we proceed with the solution

`(7000)/(3116.92)=(1+0.975\%)^(n)`

`log((7000)/(3116.92))=n*log(1+0.975\%)`

Remember here the property of natural logaritm when you apply it to an exponent.

`(log((7000)/(3116.92) ))/(log(1+0.975\%)) =n`

`n=83.38`

so the answer is aproximated 83 quarters or 21 years