Answer:
51.339
Step-by-step explanation:
Hello,
At the beginning Holly has $500
After one year
  he will get 500*(1+6.75%)=500*1.0675
After n year (n being real)
  he will get
  [tex]500\cdot1.0675^n[/tex]
and we are looking for n so that
  [tex]500\cdot1.0675^n=14,300\\<=> ln (500\cdot1.0675^n)=ln(14,300)\\<=>ln(500)+n\cdot ln(1.0675)=ln(14,300)\\<=> n= \dfrac{ln(14,300)-ln(500)}{ln(1.0675)}=51.338550...\\[/tex]
so we need 51.339 years
Hope this helps
