Final answer:
To find the principal amount, use the formula for compound interest, A = P(1 + r/n)^(nt), and plug in the given values. Solving for P gives a principal amount of approximately $905.57.
Step-by-step explanation:
To find the principal amount, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future amount
- P is the principal amount
- r is the interest rate
- n is the number of times interest is compounded per year
- t is the number of years
In this case, we know that A is $1,000, r is 4% (or 0.04), n is 1 (as interest is compounded annually), and t is 3.
Plugging these values into the formula, we get:
1000 = P(1 + 0.04/1)^(1*3)
Solving for P, the principal amount, gives us:
P = $1,000 ÷ (1.04^3)
Calculating this value gives us:
P ≈ $905.57