Question

A pensioner elects to receive her retirement benefit over 20 years at a rate of 2,000 per month beginning one month from now. The monthly benefit increases by 5% each year. At a nominal interest rate of 6% convertible monthly, calculate the present value of the retirement benefit.

Answer 1

PV= $1,394,283.42

Step-by-step explanation:

Giving the following information:

Monthly deposit= $2,000

Number of periods= 20*12= 240

Growth rate= 0.05/12= 0.0042

Interest rate= 0.06/12= 0.005

First, we need to calculate the future value using the following formula:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

We will incorporate the growth rate to the interest rate.

FV= {2,000*[(1.0092^240) - 1]} / 0.0092

FV= $3,812,441.19

Now, the present value:

PV= FV/(1+i)^n

PV= 3,812,441.19/(1.0092^240)

PV= $1,394,283.42