Final answer:
To find the interest rate, use the formula for compound interest and solve for r. In this case, the interest rate is 60%.
Step-by-step explanation:
To find the interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
- A: Final amount ($1,024.00)
- P: Principal amount ($400.00)
- r: Interest rate (unknown)
- n: Number of times interest is compounded per year (1 for annually)
- t: Number of years (2)
Plugging in the values:
1024 = 400(1 + r/1)^(1*2)
Dividing both sides by 400:
2.56 = (1 + r)^2
Taking the square root of both sides:
(1 + r) = √2.56
(1 + r) = 1.6
Subtracting 1 from both sides:
r = 1.6 - 1
r = 0.6
Converting to a percent:
r = 0.6 x 100
r = 60%