Answer:
To find the principal needed to accumulate $1500 in 3 years at a 9% interest rate compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Future value (amount we want to accumulate) = $1500
P = Principal (amount we need to find)
r = Annual interest rate = 9% = 0.09
n = Number of times interest is compounded per year = 12 (monthly compounding)
t = Number of years = 3
Plugging in the values, we have:
$1500 = P(1 + 0.09/12)^(12 * 3)
Simplifying:
$1500 = P(1.0075)^(36)
To solve for P, we divide both sides of the equation by (1.0075)^(36):
P = $1500 / (1.0075)^(36)
Using a calculator, we can evaluate the right side of the equation to find the principal P:
P ≈ $1225.34
Therefore, the principal needed to accumulate $1500 in 3 years at 9% compounded monthly is approximately $1225.34.
Explanation: