Final answer:
To have $5000 at the end of 5 years with an annual interest rate of 2%, you will need to initially invest approximately $4529.54. This is calculated using the compound interest formula by rearranging it to solve for the Principal.
Step-by-step explanation:
To determine how much you need to invest at 2% annual interest to have $5000 at the end of 5 years, you can use the formula for compound interest, which is Principal(1 + interest rate)time. In this formula, you need to solve for the Principal, which represents the initial investment amount.
Here's the equation rearranged to solve for the initial investment (Principal):
Principal = Future Value / (1 + interest rate)time
Plugging in the values:
- Future Value (the amount you want after 5 years): $5000
- Interest Rate (annual): 2% or 0.02
- Time (years): 5
Principal = $5000 / (1 + 0.02)5
Now, calculate the denominator:
(1 + 0.02)5 = (1.02)5 = 1.10408
Next, divide the future value by this amount to find the Principal:
Principal = $5000 / 1.10408 ≈ $4529.54
To have $5000 after 5 years, you would need to invest approximately $4529.54 at a 2% annual interest rate, compounded annually.