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

the value of the payments today is 14,047

Step-by-step 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*(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*(1-(1+0.07)^(-10) )/(0.07)`

`a_(10) =14,047`