or
Sophie has $40 in an account. The interest rate is 5% compounded annually.
To the nearest cent, how much interest will she earn in 3 years?
$
To calculate the interest earned in 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final Amount (including interest earned)
P = Principal Amount (initial amount)
r = Annual interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Number of years
In this case, the principal amount (P) is $40, the annual interest rate (r) is 5% or 0.05, the interest is compounded annually (n = 1), and the number of years (t) is 3.
Using the formula, we can calculate:
A = 40(1 + 0.05/1)^(1*3)
A = 40(1 + 0.05)^3
A = 40(1.05)^3
A = 40(1.157625)
A ≈ 46.30
Therefore, Sophie will earn approximately $46.30 in interest after 3 years.