A financial planner has suggested you invest in a new insurance product he is selling that will pay you $20,000 a year for twenty years once you retire. If you plan to retire in 10 years and
Your opportunity cost of capital is a constant 6% a year, what is the most you should pay today
For this investment? Assume you will receive your first payment at the end of 10 years and
Round your answer to the nearest dollar.

Question

Quizplus · Accepted Answer

To calculate the present value of an annuity, we use the formula:
PV = A x [(1 - (1/(1+i)^n))/i]
where A = the yearly payment, i = the interest rate, and n = the number of years.
In this case, A = $20,000, i = 6%, and n = 20.
PV = $20,000 x [(1 - (1/(1+.06)^20))/.06]
PV = $204,915.89
However, since the first payment doesn't start until 10 years from now, we need to discount the PV back 10 years using the formula:
PV = FV / (1+i)^n
where FV = future value, i = interest rate, and n = number of years.
FV = $20,000 x 20 = $400,000
PV = $400,000 / (1+.06)^10
PV = $135,781. Therefore, the most you should pay today for this investment is $135,781, which is option C.

A Financial Planner Has Suggested You Invest in a New