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

Answer:

the answer is approximated 83 quarters or 21 years

Explanation:

they key in this question is to take into account the word "compounded quarterly" it means that every quarter there is paid $\frac{0.039}{4}=0.975\%$. 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

$\frac{7000}{3116.92}=(1+0.975\%)^{n}$

$log(\frac{7000}{3116.92})=n*log(1+0.975\%)$

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

$\frac{log(\frac{7000}{3116.92} )}{log(1+0.975\%)} =n$

$n=83.38$

so the answer is aproximated 83 quarters or 21 years