Question

Your insurance agent is trying to sell you an annuity that costs $230,000 today. By buying this annuity, your agent promises that you will receive payments of $1,225 a month for the next 30 years. What is the rate of return on this investment?


A. 3.75 percent


B. 4.47 percent


C. 4.93 percent


D. 5.45 percent


E. 5.67 percent

Answer 1

Answer:

C. 4.93 percent

Explanation:

A fix Payment for a specified period of time is called annuity. The discounting of these payment on a specified rate is known as present value of annuity. The value of the annuity is also determined by the present value of annuity payment.

Formula for Present value of annuity is as follow

PV of annuity = P x [ ( 1- ( 1+ r )^-n ) / r ]

Where

P = Monthly receipt = $1,225

n = number of period = 30 years x 12 month each year = 360 months

As we already have the present value of annuity we need to calculate the rate of return.

$230,000 = $1,225 x [ ( 1- ( 1+ r/12 )^-360 ) / r ]

r =  4.93