# Your pension plan is an annuity with a guaranteed return of 4% per year (compounded quarterly)....

## Question:

Your pension plan is an annuity with a guaranteed return of 4% per year (compounded quarterly). You can afford to put $1,800 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?

## Present value of an Annuity:

Annuities are a series of payments paid either at the beginning or end of a period. For example, pension payments and interest paid on bonds have annuity payments.

## Answer and Explanation: 1

4% compounded quarterly

Payment: $1,800

Years: 25

Find the present value of an annuity.

PV = PMT ((1-(1+i)^-n/i))

PV = 1,800((1-(1+.04/4)^-4*25))/(.04/4)

PV = 1,800(.6303)/.01

PV = $113,451.98

Next, find the payments needed for $113,451.98 in 40 years

PMT = FV((i/(1+i)^n+1))

PMT = 113,451.98((.04/4)/(1+(.04/4)^4*40)) -1

PMT = 113,451.98 * .00256

PMT = $289.87

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Chapter 8 / Lesson 3Learn how to find present value of annuity using the formula and see its derivation. Study its examples and see a difference between Ordinary Annuity and Annuity Due.

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