Question

You want to buy an annuity that will pay you $1000 per year for 20 years. You find an account that will pay 4% per year, compounded annually. How much must you deposit today in order to fund this annuity?

Answer 1

The amount to be deposited today = $13,590.33

Step-by-step explanation:

The amount to be paid for the annuity would the sum equal to the present value of the cash flow from the annuity. The present value of an ordinary annuity is determined using the relationship below:

PV of annuity = A× ( (1-(1+r)^(-n) )/r

A- Annual cash flow

r- interest rate per annul

n- Number of years

PV- Present Value of annuity'

DATA

A-1000

r- 4%

n- 20

PV = 1,000 ×( (1 - 1.04^(-20))/0.04 =$13,590.33

The amount to be deposited today = $13,590.33