Question

You have been offered an investment that will pay you a lump sum of $30,000 25 years from today, along with a payment of $1,000 per year for 25 years starting one year from today. How much are you willing to invest today to have this investment in your portfolio assuming you wish to earn a rate of 6 percent compounded annually?

Round the answer to the nearest whole number.

Answer 1

We need to calculate the present value of payments of $1000 per year and $30000 after 25 years.

The cash inflows of $1000 will be same every year, so it is an annuity. For calculating the present value of annuity, we will use the following formula:

PVA = P * (1 - (1 + r)^-n / r)

where, P is the periodical amount = $1000, r is the rate of interest = 6% and n is the time period = 25

Also payment of $30000 is a one time payment, so we will use the following formula for calculating its present value:

Present value = Cash flow / (1 + r)ⁿ

where, Cash flow = $30000

Present value of cash flows = Present value of annuity of $1000 at 6% for 25 years + Present value of $30000 at 6% for 25 years

Now, putting the values in the above formulas, we get,

Present value = ($1000 * (1 - (1 + 6%)^-25 / 6%))+ ($30000 / (1 + 6%)²⁵ )

Present value = ($1000 * (1 - (1 + 0.06)^-25 / 0.06)) + ($30000 / (1 + 0.06)²⁵)

Present value = ($1000 * (1 - (1.06)^-25 / 0.06) + $30000 / (1.06)²⁵)

Present value = ($1000 * (1 - 0.2329986305 / 0.06) + $30000 / 4.29187

Present value = ($1000 * (0.767 / 0.06) + $30000 / 4.29187

Present value = ($1000 * 12.783356) + $6989.9589

Present value = $12783.356) + $6989.9589

Present value = $19774

So, today we should invest $19774 to get the required payments.