Question

Your uncle has said that if you agree to finish college he will give you equal payments of $2,000 at the end of each year for the next ten years. If the annual interest rate stays constant at 7%, what is the value of these payments in today’s dollars? Round your answer to the nearest whole dollar.

Answer 1

Answer:

the value of the payments today is 14,047

Explanation:

this problem can be solved applying the concept of annuity, keep in mind that an annuity is a formula which allows you to calculate the present value of future payments affected by an interest rate. by definition the present value of an annuity is given by:

$a_{n} =P*\frac{1-(1+i)^{-n} }{i}$

where $a_{n}$ is the present value of the annuity, $i$ is the interest rate for every period payment, n is the number of payments, and P is the regular amount paid. so applying to this particular problem, we have:

$a_{10} =2,000*\frac{1-(1+0.07)^{-10} }{0.07}$

$a_{10} =14,047$