Question

You are offered a court settlement in the following terms: you will receive 7 equal payments of $7,275 each every year, with the first payment being made 3 years from now. The current annual interest rate is 7%. Assume yearly compounding. What is this settlement worth in present value terms? Enter your answer in the form of dollars, rounded to the nearest cent, and without the dollar sign ('$').

Answer 1

$34,244.98

Step-by-step explanation:

For computing the settlement worth in present value terms first we have to determine the future value which is shown below:

Value at year 4 = Annuity × [1 - 1 ÷ (1 + interest rate)^number of years] ÷ interest rate

= $7,275 × [1 - 1 ÷ (1 + 0.07)^7] ÷ 0.07

= $7,275 × [1 - 0.6227497419 ] ÷ 0.07

= $7,275 × 5.3892894016

= $39207.08

Now the present value is

As we know that

Future value = Present value × (1 + interest rate)^number of years

$39,207.08 = Present value × (1 + 0.07)^2

So, the present value is

= $39,207.08 ÷ 1.1449

= $34,244.98

We simply applied the above formula so that the present value comes i.e today's value