Question

Your pension plan is an annuity with a guaranteed return of 4% per year (compounded quarterly). You can afford to put $1,900 per quarter into the fund, and you will work for 40 years before retiring. After you retire, you will be paid a quarterly pension based on a 25-year payout. How much will you receive each quarter? (Round your answer to the nearest cent.)


Step by Step answer with explanation please

Answer 1

You can use the Annuity formula to find the PV (present value) of those contributions.

The formula for the PV of an annuity is:

PV = A/R - A/[R*(1+R)^N)

where R is the periodic yield, A is the periodic payment and N is the number of payments.


Let's look at an example. Suppose that you want to invest $25,000 now and you will contribute an extra $5,000 every year for 15 years. Suppose that the interest rate is 8% per year and it compounds quarterly. I made this more difficult to illustrate a point.

Let's find the PV. Since the annuity is annual, we need an annualized rate (annual effective rate). The 8% is nominal, not effective -- so we need to find a rate that includes te effects of compounding. The quarterly rate is 2% (one fourth of 8%) -- so we can get the annual rate by looking at:

R = 1.02^4 - 1.0 = 8.243216%

The annuity is for $5,000 per year, so the present value of that is:

5,000/0.08243216 - 5000/ [0.08243216*1.08243216^15] = $42,169.08

We need to add the $25,000 contribution we now make to get:

PV = $67,169

We can now calculate the future value in one of two ways -- compounding 2% quarterly or compounding 8.243216% annually.

FV = PV * 1.02)^60 = $220,383.83



So, just use this to calculate your numbers.

Answer 2

What about the 2nd part of the question?

Answer 3

So, just use this to calculate your numbers.

Answer 4

That is very vague, what numbers go where after retirement in the question?

Answer 5

https://answers.yahoo.com/question/index?qid=20111214141437AAI76Im

Answer 6

I saw that like half an hour ago, that doesn't help me at all