how long Will it take for $7000 investment to grow to $7553 and the annual rate of 3.4% compounded quarterly assume that no withdrawals are made

Answer:[tex]t=2.25\ years[/tex]  Step-by-step explanation:we know that    The compound interest formula is equal to  [tex]A=P(1+\frac{r}{n})^{nt}[/tex]  where  A is the Final Investment Value  P is the Principal amount of money to be invested  r is the rate of interest  in decimal t is Number of Time Periods  n is the number of times interest is compounded per year in this problem we have  [tex]t=?\ years\\ P=\$7,000\\ r=0.034\\n=4\\A=\$7,553[/tex]  substitute in the formula above  [tex]7,553=7,000(1+\frac{0.034}{4})^{4t}[/tex]  solve for t[tex](7,553/7,000)=(1.0085)^{4t}[/tex]  [tex](1.079)=(1.0085)^{4t}[/tex]  Applying log both sides[tex]log(1.079)=log[(1.0085)^{4t}][/tex]  [tex]log(1.079)=(4t)log(1.0085)[/tex]  [tex]t=log(1.079)=[(4)log(1.0085)][/tex]  [tex]t=2.25\ years[/tex]