It would take Sarah 0.15 years more than Brandon to get $1,530 in her account.
Step-by-step explanation:
Step 1; First, we need to calculate the interest per year for both Brandon and Sarah.
For Brandon, if 3[tex]\frac{3}{4}[/tex] % is compounded monthly, then yearly interest = 3.75 × 12 = 45% is compounded yearly. So 0.45 × $510 = $229.50 is compounded annually.
For Sarah, if 3[tex]\frac{5}{8}[/tex] % is compounded monthly, then yearly interest = 3.625 × 12 = 43.5% yearly. So 0.435 × $510 = $221.85 is compounded annually.
Step 2; If money is three times $510, there would have to be a balance of 3 × $510 = $1,530. As they have already invested $510.
The money needed by interest = $1,530 - $510 = $1,020.
Step 3;
As Brandon gets $229.50 every year, years taken to get $1,020 = [tex]\frac{1,020}{229.50}[/tex] = 4.4444 years.
As Sarah gets $221.85 every year, years taken to get $1,020 = [tex]\frac{1,020}{221.85}[/tex] = 4.5977 years.
The difference in years = 4.5977 - 4.4444 = 0.1533 years. Rounding this off to the nearest hundredth, we get 0.15 years.
