Question

You decide to invest $1000 at the beginning of every year. If your rate of return is 3%

compounded annually, how much money will you have at the end of 5th year? Please provide step by step

Answer 1

To determine the future value of annual $1000 investments at a 3% interest rate compounded annually over 5 years, apply the formula for an annuity due to calculate the total amount, which will be $5,309.13 at the end of 5 years.

Step-by-step explanation:

Calculating Future Value with Annual Investments

To calculate how much money you will have at the end of the 5th year with a 3% compounded annual interest rate after investing $1000 at the beginning of every year, we need to use the formula for the future value of an annuity due. Here is the step-by-step breakdown of the calculations:

1. Determine the annual investment, which is $1000.
2. Identify the annual interest rate, which is 3% or 0.03 in decimal form.
3. Recognize the number of periods, which in this case is 5 years.
4. Apply the formula for the future value of an annuity due: FV = P × { [ (1 + r)ⁿ - 1 ] / r } × (1 + r), where P is the annual payment, r is the annual interest rate, and n is the number of periods.
5. Plug in the values and calculate: FV = 1000 × { [ (1 + 0.03)⁵ - 1 ] / 0.03 } × (1 + 0.03).
6. Compute the future value, which gives us FV = 1000 × { [ (1.03)⁵ - 1 ] / 0.03 } × 1.03 = $5,309.13.
7. Therefore, at the end of the 5th year, you will have $5,309.13.