Sasha will deposit $450 at 6% simple interest. The formula for calculating the balance of an account with simple interest is given by A = P(1 + rt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), and t is the time in years.
In this case, the initial principal balance P is $450, the annual interest rate r is 6% or 0.06 as a decimal, and the time t is 2 years. Plugging these values into the formula gives us:
A = 450(1 + 0.06 * 2)
Evaluating this expression gives us a final amount of approximately $477 in the account after two years.
Sasha will deposit the rest of her money ($850 - $450 = $400) at 2% compounded annually. The formula for calculating the balance of an account with annual compounding is given by A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per unit time (per year in this case), and t is the time in years.
In this case, the initial principal balance P is $400, the annual interest rate r is 2% or 0.02 as a decimal, n is 1 since it’s compounded annually, and the time t is 2 years. Plugging these values into the formula gives us:
A = 400(1 + 0.02/1)^(1 * 2)
Evaluating this expression gives us a final amount of approximately $416.16 in the account after two years.
Therefore, there will be approximately $60.84 more money in Sasha’s account at 6% simple interest than at 2% compounded annually after two years.