Annuity interest rate Your parents just called and would lik

(Annuity interest rate) Your parents just called and would like some advice from you. An insurance agent just called them and offered them the opportunity to purchase an annuity for $14,217.56 that will pay them $2,500 per year for 20 years. They do not have the slightest idea what return they would be making on their investment of $14,217.56. What rate of return would they be earning? (Round to two decimal places.)

Solution

Let the rate of return be x%

At this rate;present value of inflows=$14217.56

$14217.56=2500/1.0x+2500/1.0x^2+.............+2500/1.0x^20

14217.56=2500[1/1.0x+1/1.0x^2+..........+1/1.0x^20]

[1/1.0x+1/1.0x^2+..........+1/1.0x^20]=(14217.56/2500)

[1/1.0x+1/1.0x^2+..........+1/1.0x^20]=5.687024

Hence x=rate of return=16.80%(Approx).