Lily puts $200 into a savings account that pays 1.8% interest compounded annually. Write an equation that can be used to find t, the number of years until Lily's account has a value of $250.
The formula for compound interest is given by: P(1 + r/n)^(nt), where:
P = initial amount (principal)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, we have:
P = $200
r = 1.8% = 0.018 (as a decimal)
n = 1 (compounded annually)
The desired amount is $250. So the equation becomes:
$200(1 + 0.018/1)^(1t) = $250