You are saving for a new car. You place $11,100 into an investment account today. How much will you have after four years if the account earns (a) 3%, (b) 5%, or (c) 7% compounded annually?
To calculate the future value of an investment, we use the formula:
FV = PV(1 + r)^n
Where:
FV = Future Value
PV = Present Value (initial investment)
r = interest rate as a decimal
n = number of compounding periods
(a) At a 3% interest rate compounded annually:
FV = $11,100(1 + 0.03)^4
FV ≈ $11,100(1.03)^4
FV ≈ $11,100(1.1255)
FV ≈ $12,506.05
After four years, you will have approximately $12,506.05 if the account earns 3% compounded annually.
(b) At a 5% interest rate compounded annually:
FV = $11,100(1 + 0.05)^4
FV ≈ $11,100(1.05)^4
FV ≈ $11,100(1.2155)
FV ≈ $13,470.55
After four years, you will have approximately $13,470.55 if the account earns 5% compounded annually.
(c) At a 7% interest rate compounded annually:
FV = $11,100(1 + 0.07)^4
FV ≈ $11,100(1.07)^4
FV ≈ $11,100(1.3108)
FV ≈ $14,533.20
After four years, you will have approximately $14,533.20 if the account earns 7% compounded annually.