Question

Please show calculations with Formula or financial calculator, excel not allowed.

You will invest $7,500 at the end of each of the next 6 years, and $15,000 in years 7 though 12 in a project. You will invest in it $25,000 today. If other investments of equal risk earn 9% annually, what is its future value?

Answer 1

To calculate the future value of the investment, apply the compound interest formula to the initial lump sum and the future value annuity formula for the set of annual contributions, making sure to consider the timing and amount changes of these contributions.

Step-by-step explanation:

Calculating the Future Value of an Investment

To find the future value of this investment, we will use the future value of an annuity formula for the regular payments and add the single lump sum investment's future value.

Firstly, let's calculate the future value of the initial $25,000 investment using the compound interest formula:

Future Value = Present Value x (1 + Interest rate)^number of periodsFuture Value = $25,000 × (1 + 0.09)^12

The first set of annual contributions of $7,500 over 6 years can be calculated using the annuity formula:

FV Annuity = Payment × [((1 + r)^n - 1) / r]FV Annuity = $7,500 × [((1 + 0.09)^6 - 1) / 0.09]

The second set of contributions of $15,000 from years 7 to 12 requires us first to discount back to year 6 and then apply the annuity formula:

FV Annuity = Payment × [((1 + r)^n - 1) / r] × (1 + r)^tFV Annuity = $15,000 × [((1 + 0.09)^6 - 1) / 0.09] × (1 + 0.09)^6

Finally, add up all the future values to get the total investment value at the end of year 12.