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Brayden invested $510 in an account paying an interest rate of 3 3/4 % compounded monthly. Sarah invested $510 in an account paying an interest rate of 3 5/8% compounded continuously. To the nearest hundredth of a year, how much longer would it take for Sarah's money to triple than for Brayden's money to triple?

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 % 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 % 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 = = 4.4444 years.

As Sarah gets $221.85 every year, years taken to get $1,020 = = 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.