After 10 years, Emily's balance will be greater.
To calculate the balance of Rose's account after 10 years, we can use the formula:
balance = principal * (1 + rate/n)^(n*t)
where:
principal = $80
rate = 1%
n = 12 (monthly compounding)
t = 10 (10 years)
Plugging these values into the formula, we get:
balance = $80 * (1 + 0.01/12)^(12*10)
balance = $80 * (1.00083333)^120
balance = $80 * 1.1037597
balance = $87.50
To calculate the balance of Emily's account after 10 years, we can use the same formula with the following values:
principal = $50
rate = 2%
n = 52 (weekly compounding)
t = 10 (10 years)
Plugging these values into the formula, we get:
balance = $50 * (1 + 0.02/52)^(52*10)
balance = $50 * (1.0003846)^520
balance = $50 * 1.483529
balance = $74.18
Thus, after 10 years, Emily's balance of $74.18 is greater than Rose's balance of $87.50.