Question

You’ve won $1 million but aren’t receiving it all today. Rather, you get $100,000 today, then $100,000 every year for the next nine years. Assume that you could invest a lump-sum payment today in an account yielding an interest rate of 3% annually. What’s the total value of the future nine payments today? Round to the nearest dollar.

Select the correct answer.


$778,611

$876,711

$878,611

$1,000,000


What’s the total present value you will be paid?

$778,611
$876,711
$878,611
$1,000,000

Answer 1

The total present value of the nine future payments of $100,000 each, with an annual interest rate of 3%, is $778,611 when rounded to the nearest dollar. This uses the present value of an annuity formula to discount future payments back to their value today.

Step-by-step explanation:

To calculate the present value of the future nine payments of $100,000 each, given an annual interest rate of 3%, we can use the formula for the present value of an annuity. Since the payments are made at the end of each year, we must discount each payment back to the present at the given interest rate.

Step-by-Step Calculation:

1. Identify the payment (PMT), which is $100,000.
2. Identify the annual interest rate (r), which is 0.03.
3. Calculate the present value factor for each payment using the formula PV = PMT / (1 + r)ⁿ, where n is the number of years until the payment will be received.
4. Sum up the present values of all nine payments.
5. Round the total to the nearest dollar.

Following this method:

• PV = $100,000 / (1 + 0.03)¹ + $100,000 / (1 + 0.03)² + ... + $100,000 / (1 + 0.03)⁹

After calculating the sum of all present values for the nine payments, you will find the total present value is $778,611 when rounded to the nearest dollar.

Therefore, the late-future payments have a total present value of $778,611 today, and this would be the correct answer from the given options.