a. The value of N is approximately 10.25 years
b. The value of i is approximately 7.98%
c. The value of P is approximately $116.10
d. The value of A is approximately $304.04
a)
Formula: Use the future value formula: FV = PV * (1 + i)^n
Values: P = $1,000, A = $200, i = 12%
Solve for n: n = ln(FV / PV) / ln(1 + i) = ln($200 / $1,000) / ln(1 + 12%) ≈ 10.25 years
N ≈ 10.25 years
b)
Formula: Use the future value formula: FV = PV * (1 + i)^n
Values: P = $1,000, A = $200, N = 10 years
Solve for i: i = (FV / PV)^(1/n) - 1 = ($200 / $1,000)^(1/10) - 1 ≈ 7.98%
i ≈ 7.98%
c)
Formula: Use the present value formula: PV = FV / (1 + i)^n
Values: A = $200, i = 12%, N = 5 years
Solve for P: P = FV / (1 + i)^n = $200 / (1 + 12%)^5 ≈ $116.10
P ≈ $116.10
d)
Formula: Use the future value formula: FV = PV * (1 + i)^n
Values: P = $1,000, i = 12%, N = 5 years
Solve for A: A = FV / n = ($1,000 * (1 + 12%))^5 / 5 ≈ $304.04
A ≈ $304.04